{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problem 9.1 (Page 38)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import helper as hlp\n",
    "\n",
    "X = np.array([[0, 0], [0, 1], [5, 5]]).astype(\"float\")\n",
    "y = np.array([1, 1, -1])\n",
    "#(a)\n",
    "knn = hlp.KNeighborsClassifier_(1)\n",
    "knn.fit(X, y)\n",
    "hlp.draw(X, y, knn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#(b)\n",
    "scaler = hlp.StandardScaler_()\n",
    "X1 = scaler.fit_transform(X)\n",
    "knn = hlp.KNeighborsClassifier_(1)\n",
    "knn.fit(X1, y)\n",
    "\n",
    "hlp.draw(X, y, knn, flag=2, preprocess=scaler)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#(c)\n",
    "pca = hlp.PCA_(1)\n",
    "pca.fit(X)\n",
    "X2 = pca.transform(X)\n",
    "knn = hlp.KNeighborsClassifier_(1)\n",
    "knn.fit(X2, y)\n",
    "\n",
    "hlp.draw(X, y, knn, flag=3, preprocess=pca)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problem 9.6 (Page 39)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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vwldVo8letNR4Q8QWQPd49Kw0068FfJoPj62HKzJgdNP9ex4cHA4gti2UlrrqWr2xiFTXXl9U1Rejn6cCJwE3AIswy5PtFkfoHkzMKDHmgArblB3pHgfXNYNzm1SZafNC0G0OekYqHJOMPr4B1gSYfu+7zEl+gSZ2D07jfdz4gKigjWC8DiplcJwFLqNBy6VL4e0UeKuTGcNZixHF2IYHNjLmhxrQSo8GF8ZG7OBwkGIrBOuu6eap6u4W4f07cLWqFovILcClwIu7qet4LxxUHN8IWu7gG+sR8AnEiAlqKI3A4nJYVmGu3mVLoUccvNTRaKIfGfezuS3+DwQKrBXkMr/K+0AxQleJunwpvN4JbmmBBNUkPf843zwAXGwfQLEmUOPw1dZqbbNrjwcHh4MEtY3QrUuphRSgh4i4gCPZ/lezE47QbWjCCv/eAA+tNQJ2UR94oKWxnya6YGEvmN0bHZYCL3WAa5tDGx+cshDpOwexgHOamH0FaOYFn9D652xcGoO3NI6UianwQ7HRQivvH1thcQWS8hOyoAxJrvaaFQHKIpDgghuamSCK1l64dRV8kLf7Y3HWBnE4hFCtN6H7CEazLQJSgXE1VXbMCw3NsxvhzjVGCG4Owl2tYVp0qR1/BD4sgNtawlNtwSXmMVkQRtaHYH3IRIQ9nGle6QVYXgHL+zD0mUco+nAF8V8n4FmcA5oDL3VALmiC2hF4MxfuXmP8cR9aa4R1FPFgvCDcAk+3g6uaQfavsDYI5y4Bf1qVt0N1NgUgxWPGKSDiPNMdDl5UhWBw3+9RVZ0BdKtrfUfoNjRlthG4EeDjrfBiTtVVCQOp0ZDdZBe8ngONPfCPdShRpdWvcPQ8eL6d8Tq4czVkeJHve9AolAmNNsBda83EXLrbaLuD5iPzytEsHzqrt9GSj/rVtOez4NtukOapss8muYxGHSOQ7tlO4GqkyobL+UtMwEeCC9r70NEZANv79jo4HCTontl06429Eroicg1wTvTPRsD0HR2CRcQNrIwWgOtVdf7eDvR3y83NISdofGhfi4boRh221cK4boVts5y6jfHb9dsQKxBNwCwVNly+HI0oYoOuDxr3sDg33NwSXtgE/9cJjk4ywr1XgpkYu7opNHYbIVoUtQ24gM8L0eG/GQE8qQd0iEWn9kSmFMMZaduGrqrmwQBgg7TzmTwMgE7sUnUcLkXcjuB1OLiIRKC09MC/je3twpTPAc8BiMgYzHLrO9ITGKeqf9v74f0BiHPBM+3M59IITMyv+i6CSSITUDPB1iUOfiuHt7dAiY1G7fXqUugQg7SOR78shNEZEGsi1bAElh6xfZ+DG5lFK38qgcuaopEIG89ZRrOxLbHcXuTHYqQwgkoEXt5szBeHxRthXZ0dpwte7GDabhVjwoLt3dRzcDgIUIVg6MArA/sk5kWkBZCxm+iLfsBIEZkhImOjmq/D7vhsK5ycQtSzy8ipoxKNAHtsPbSdaeyqveOhzEYAif4jAot+WAgTO0Npf/hPezNBt7TCaMnVk+IIxkxhg4zLhWELCFolpD95Bt8vGM/Pa79B/9TYaNkAK/wwZsMuw4zFEqMZW5jJthgLLs6AQY22f5xH5+i25XFw8vY6HARU2nTrUuqTfW3tOqIa7y74BRiiqkdgfpIjdqwgIleKyEwRmZmbm7uPQzmEGZ8LZy+Ga1ZA+1ho4UHuagnf9DD23sc3ICE1LltXr9i2m0b/CULbSztC8s8wbAEUhUz6x3UBoyVXRq9FFCIR5NvCqr6zE4g5dT2e9Hn0nnQxqbFd4ZKmsKYvDE5GphUjJ6fudujiFsQjO9ltRQSJiZbK76I5ewnhCF6HBqcyIq0upT7Za+1TzNT0IOCu3VSZp6qVjp0zgQ47VohGdLwIkJ2d/cf4FY7PhR+KTW6E5zbDmzlQWC0QYmGFUXNf34IA+o/10VA0MYETUPXaHkUQfB8bJVanlMC5i2FuGdzTytiLz25i2vDb0Gs2lFU71ZMKYFUAKbOJu6McuTyqljbxwifdjE15Ry03rDAqGsU2ph0MTanbsds7fHacGxwaEFGIaYCJtH257Y/BTKDtTli+ISKHRR2GTwPm7kNfvw9+LYVRy+A/m4zHwQubthe4UGX/XBeEJzaYaDDYZr+FqHAFIwy9UuXJUMmiCiixTUKc89OjPrxiotfyw9uqaYoL7muDLWFCcX4291vKz+5/VGtIYHUAhi6AS5aYBDxglhf6Xz46NAVt5DYeDHWh8hEvbDM5ODg0FKLgDdet1Cf7InSHAj8AiEhXEXloh+8fAN4AfgV+UtXJ+9DX74PqwQmFkdqXAUlxY7urIg7UAqwquSwKtPNBMw/qokr4lkXg4iYmgk2iQROqRuj5rKoxnNUYjm9ExTOpWCE36bPa0vaHAVUC0Q1cuxwmFZrcuy9tNtuzfGjrGHgo00yu1TX6TDDmBq/sOhWlg8MBxGVDUqBupT7Za6Grqneq6vvRz7+p6t07fL9AVXuqag9V3Z0J4o/FYfFwYbpJswjm7HfxmbSOO6Aoywb+wEeTH6QoKwdBsKJKsVBN210WgNtaEj4rEb0kDe0UayLX/tkWNoegMEQ0UgGyfMi6vjAmy6RoXB8EgfgXI7hCbnx5iRw16pyqyLIwaKdY7Fhlc79lVLQpM9u3hkznN64wARzlkZ1MHtsdiyoaNMl1GmJ5FAeHXWEBMZG6lfrE8Sg4kFy5HN7L2942uz6wnY01FOvns08eJ+/w1diuMOG4EEuv+JEj7jzTVFDQmKh91wbCSvkLc3lz/p9xebycEnyPlKJYCp6bRJOHEsFlwbc9oFcCElD4sRhuWw2WELm2EaGEEnwDk9CfSwBBrmxeNV5VuLkFX11/H+va/Izl8nJO5GviL1qHrA6gyytMKsrFFch9rU0inl2wSr+gpR6LhzhjirCixx4hmjAdR/N1OOCI1r9ArQuO0N3fRBQuXALfFxnbaplttEw3JrCgNOprOzIVRmWweum7bDliBeGEACi48NH8ytPQRy0otk1o7rudzUTZE+uRcptZD3yI7Q1ha4iSsb8Q+8wqfP4wEkgk4gqx5vWptD09FXJC0D8R/EpRu81MGHQZYSvI0RlX0e38U+GCdONnWznuL7bCjSvZsHYWYfHjVoutkSXEZ6agOUEIKPLxVmOyqEGD/Uke5jT6AEKYMmJDjau+VKoi2hwcDiCiEFPP9tq64Ajd/cmtK+GlHOM1EFLjCQAmh62Aumy+/89Ycoav5KzUb7A8btKCg/HJq/hLt9Lc1Z8B1sMkaTM4dpnx5f2pJ3RPgGOTzSoQsS6af7SCRZFJeMrjaHtjRyQMEVeYiCdMRZyfv512K++NfRFNdptVJWaV8tuV3xOMKwdR5g2fQEl4HVkJZ5HhPc4IwoHz4ecSGJ1O39At/Ox5lDTtQjM9Asa7YXwedPLBO3mQFQPn7VrLBWgiPXjPO4xkO5Mh4TE7V3C8GBwagErzwoHGEbr7i5wgjNlUZUoACFb7rJDXbS29nhhJ/DuZyOdG1UvxdOCC4DQKnvqWRlZbrNFN4f1c+G6r2WnYQlTDrHh7BRkdjyYpsz3tBl9AwTtLyEjuDz4LOxwmkFjKi0tuoMQbIG5RHASAV9vBgCRKpgRIDl+J2z+ZsK+U4sxcfr31QxYEv+BiZhFTkQCZMTC7BHUJPXQ0PQKjo8ZkgSQo6phCyZQgsUNbkHZW7Pbmgf/lw+RC+HMz6BzHEJ5li8whUVoTR1Q4R9TYhlt4HdOCQ4NQOZF2oHF0jP1FihuaeKomzXZB0uoMEtan4e6Qsp1AlhgXqZcei3V8Y7NK8A0rjRnCNm5fVj4kPBDm/ZQzsM9fDJctp3fx1TQ/J4EQ5Ux79A3Gz/sb3kYhGsdbDItpbK50dgIsqaCkayrxBW0Ycs+3tPr5bESNh4OtEezVpWZ14o+2gstCbmwO/94Ipy+CjjOhLIKqUjQpiF0O5bPDhHOrzaItLjeJb/6zCYYsAMDCRVOyiZNq2nBEofts5Ifi+j7zO7GBabxGNh9wGgGK9nt/DocGwqHnMuawK/y2iQbzWjCvN4zrDL3jdqqmFniLY3H53ejHW2C133gBVESzjmV4oUcC9EuMenhFtUGBUJyf9UPmE/CVoO9ugXfzcD2VgyvoxXYZz4L2445GFFzlbkShvGWxSYLTO4H4ChMeLOIiv/0MmsxvR6svezHwhqtxN05CF5dDuY1aoMv8yD/XEfk2h5XHTmHrwlnggqTjvIgXxAuupGq3UdS2q2c3Rh/L2i7yTCQaNjy/DM5fgpRG4IciNjGDJUwgjH+/XJIfuZ9ycshlIcv5eL/04XDoUTmR5ngvHMosrzD5EcpteLYdXNkURqbC4GSjPX5fZIRSBJMNDBAs2GzDYXPgzY7wST7c1cYshe4RSK+8RCbcV1VY9ehS1oxcwAl/ugHLFgSwVweQY5OJWRND/zsuQEJC2wlH0OynjuT3WMfn7z3OGe2Gg60kv9QS10crGXf6SCK+csobw5CfH+bb5x/ge+tlznj5NdKu98HhCTCkEYxuyqRjb2b94AWc7j4JbEge7EV6FpGY3ATLV8080D0efaMjnJhiHjwhoNpiGOIWKA3DlCJoEcPGy9fwKaMBYQ1fc+Juo8prRu1oxjMB3Nt7QzQlmyJWAzZpdN2r9h1+f1gKMeEDb9R1NN365LOCqkmz5zZVbY91wWfdzPpm3iphsM3X1ivQ0muSf/+5BbyVY76wBF7vTMmIAIGUMsK+IPnDN9F4cVvO6HA3WZ/0pVIDjnj8Jmz3kUws8SIRi6bTOyBqkbQyg4Rck9uWoA3FEbynZRCJKd82kJX9fyRiBYjgZ96JE2F+H3itE3gs9PFM8k/KIRwfoBFtTZIdgS0Z05ifOHbn83B62k6LYG7HwEZQ2B/W9KW42WaMV0MFhazY/T61EabKE2IHn+EBPMBQXuBMPqEph+99Hw6/KwQlJhKuU6mxHZFrROS7aPlVRF6oqb4jdOuT4SnGfcorcE2z7b/7dCs8u2lbDlyoFkGmQJ94OCkVshPhjtZGeKtCRFl/8WLeXnUrE2bcxaLzvyblvKPQZf0puykT7RmHAu5yn/GWODkVhqWYMUQsIp4w6o5wWK8bjdlipR+S3HgDcRxrP4qHeLozim5ciIsYXMTQUU6vujMiCuPzGDz1QbwkU2Zv2hZ9liO/ssn+eadoNLHEvENVZh+rgfacTGuOJ40uHMc/9/rUbxcHvcO8nIWL1gwklU57377D75AwZuHeupTdo6rPqepAVR0ITAFeqqm+Y16oT9I9sCbbOP1HV3wILchl/sJn8cWk0SXcy5gTwCQhF9ByNZqxR4ygXVZh1iIrCcM/syhrXUKHV48ieLKHwOzl9F50GZwSjxVjEXdSIvLG+m0yRl/JoeKBRDZ5PqdZo47EbmmE4Mb75ywyUloZzbldrBFKNnQNn0c31wXbhn8JswCIIbkq18Mdq+Hlzax4bDyRARXkyyISIs2xrRBBu4hs101VIXLVEJfU6HtbKajd4mMoz+/TaTcNsW3Jon1ZqWKrncsyeyG9Xf3xSkztOzgcwgRgX96udqCWVLfbcIRuffH0BhPp1cgFc3qb5emAqfNvZenpU7BsC/nH1XS5vb8569U0XgH0kwKYN8/YOzeGzNI4yyuIP7oFnOyiZ2A0DLahIBe1gQob+bkYUtxornn90RMa8VXocnLHLsJd4eW8jk/i/r/DkGaxJgWDqsnL8OFWSLTgnCYmLNdlbKAxJKOqbNKZhF3ltNAByCIzqZa4rDF97j2d6dc9hDshhla3teL4vz8Oqe5tArdSkNbmAqZRuzaAerRelvPZNkm3DxTY+Qwr7URIg3R1Hc5bCT/s87gcDmYqNd060VhEqgvTF6NZEqtTU6rbbThCt754dpOZJCu34asCsxz6t4UEPWWoO4KGhGBhMeoVSHYhueFtNl21gAwPsrSiKpdYUOGeNdDCa5Zmn1wAY3Pgy0IYm0NkRBrup9ajGia8tDueAi+RLhYuXwJhT4BIfITP5jxNj8yrSXs3nZRufcHrIlxawcQrLiRLh9I3cquxz9qA10xGrQtP4UvP5QAcHv4zff5xKazy0/PZESg2HT8bSMw3fSBvA5LuNtozoJVhyRgHicj0AAAgAElEQVRBatI9bC9M19kr+Sr0PudzLT5iCeNnob5ONy7GQ+wBuEg1s9ZeTlCDVFDGvMiMhh6Ow34nwh4I3TxVzd7dl3VIdbsNR+jWF1dkwD1rzeoJlaG000oY8OwoXOUejrzvPBJWpSIo5Ia32XOLD8/H064xseEEdO1WRKOTawqSG0bnlpmJp0mF8HWReZNfUI78Vg7dY/Ff42WW93F69LwS35oEmrbpS757CZ0iZ9Gi+QB8oWRmtnmcwfkvIGk+ZkYep8C1hGJdTQf7VFK0g8nnEDGz/81X9OKSE55Hy0LMuftT9InfoDRizAVBi4TipvBj2HhZLCqHbvHmWKtPXoXYyZ5rq83ZpUdSokUstebzsPclAhSz0HqLFNrThsH7dPq3CX0LxLN3mnM3Vx+OdA9kevg7/hzz930aj8OhQBgoqK/Gakt1uw1H6NYXf20FozIg0WW8FQD6JRL/9xSGXPJnVKp5K5ySCp9sJeeIVUybPJGRrrfRCg/adR3WwxugQyx0iUMnFUJT49WgClKZ1tEL/HAYdItD31nC0TddhLyTBW2UbL2J7ODNqCoBivBJI9r/MJDXLssmeWFTSg4rwKUxCC68mswWmUcT7c433Mxa73eMePMBMjY1RtTL4S+faZYLmluG2oq/n4vA4i3EnVlMRXKA5NbVbJ6VSWwAfiuDExagtiJfdoe+iUSIUKJFhAnxmf0uh7uh2PoJS9z77MalWqVlY5u/9ybKzS1uXoj/ZJ/G4nAosUeabm1sS3VbG47QrU/SvVWfX9kMly3flvxWNGpGyIyB6SWQ7MI+PoE0T3fUVjbE/8SSq8aRoc3odssdgMCcEioenkucgqS44bIMkwh9hR8GzINhKcQ+lcmSxWPo/FYarA3CLS3AC7KgDN/JSyA/TNZdJ5D16jBo7uX9nuPpEE6ghfanlCL8kkc+i1hlfUFYKvjl+JcY+fidlDTfgjUgA8/XISSkaJzFyrvLGd3nQjrObENe91I+T1xWdbyVE1lhTHBIQE3ww1Mb4e1OeMTDk7HjeDnwGKd4L+Rs17VsYS5JtCaOaglwHBwOGHtk060RVb2zrnUdobs/WOOH0cu326RRTVBWBtCjk2BOKU3HNicjpwsFZZP57LWbsFuGWfYgVPhj6eu6DbrFE/e9C/luORpnwaUZMDgF5mxAwgqfbMXu48O+KA3NSkPCAjevNEurHzUXiboX6kProPRoAErWl9Pm+t54YkuY99x6Biafip9CLDy4gkJxlyA/vbCQBec/CiqcNudNmtyZyOwzlzLuuA/pwRFknLiUIe5MtrKUd/zj+S78KdfH3McATjQd9kuC21vCw+tgZNVSPkO9ZzLUe+a2v2v0mc0Lmci1/knGDa8GRAT1VjMvOLkcHOpE/Xov1BVH6O4PJu9gJ4oBXusI5y41E2flYaxyG/XbsCyAbi1Dsbd5AeQWzIFIEO5cBSrosUmQH4Kxm02C8o4+dGE5gbZBvjjuakLuIAGrgt6ua6Cjz0R7hY3VWFG0hXebR9cF947A9dVW1CqnW+cMPr37HYbIaZwTnMziCb+QsvAIZl98PRFfCGz4Ju0Wyj/183R4Kf5IOR5cjHKnU24tY6KeyguBtfgp58bys5kVZ/IaTOd7br/2ElpdmcVzjT+hcuH2bV4LteXQLQpDl1kmJLpbHEzvVesprw/vBYc/GvWn6e4JTnDE/uC1Ldv/HQCe2ABXZ/Djk6+zctRs1CcQI8y45k2SilvS96sr8BbHk7i2Cf0uPwtO/w0ae+CfmfBxN5jRG6YeBvNLYUk5pLqY/dAnDLjpEk7Pvpf2R2fiX1rARSecTcn981FRAsllFLXLYdPbVUll3C3iCTeNp7h/UyYkvs/dwSt44rdLyb/1E1Lzbey0MtLXHYkVcBNTGM8Jv/2Lc9d9WeWZUNmQGpH+qncyjUilFSlQOghKuvBw+Eo2WeuY5/2Fz0Pjq85DpGrfmlaaMHkobJN7eGZpdGFOB4f6ptKmu2/BEXuKo+nuC0VhGPmbERJvdoLjks32LB9MKdmuqswsI7y0mLz/rabbUX9DB2Zgx9nkNXuOounF9Dr7GA73H2fyKwBIGSS54MIM4xGhCr+UwGMbzYRcboR+552KIIhtkbjQw5fzJ1LeoRBPyIOlFp5SH6/nX8851tfbtEq9vzWbScVWGFx8Ky/5X+T6084laX0qEV+I92eMYmvntbT+qDfDzrwVaetFFzTmpXWTeGvTCwxyDScy4G3K7VwGh58m3Tqcx3xvcHhoOmgQvI3pybesYxOKTQfpVnUSqk+2VVNyIxrhlcCTFGoeV/nuJLF7komq+7IAbm/JzMiPrLaXMsJzDnESv58upsMfDgmDu47eC7WtZ7gHOEJ3X3gnF2aVmtfgQfNNGHATN7yRu101FWB0Bi5bOXn4nUTyMqBTHBbQKjSQPN9CUqQvYJlIMAFiXejGAHLzSnizk/F++GRrlQcEimW7iLjDuGwLRqYx5LzLeCbwNPayPtjxiaye8wFq2dihMCFvGW7iUJeFWoJEwG17yLI74QnFGLcxQMNmwN5yn/HhjRUIKx3XHc4tk8YQf7iH1MA52wWgHeseDrQCd1vAzX2R6+nzxUekrWmB3c/D/b2vY5T3ZjLcaXxv30XapONpsWUIjYcn4mniYkJoLGMCfydMmM26gSfi3qRooo+V/EpxeA03lF0GwKTQB7wQ//vIErZmTSEXXPA+MTFuxo07k/R052FywJEIeOqoxTpC9yChZ3zVq69iEt5UQytX4XVZcEETs05ZihvX9AAcFQdhpSvn4brDB3dB+NHlzJP/o2eXPxPwFhH3iQve2Wrsm/9uC39piU4tpjB9PZPefRpPqY8j7zqPjD7HYN2ZhUtdvFs6hdgmyQhCm6NOp1NkFjNdT7GM/5FBb07zTqTxhT5KfgyR1tfH+81mUPHZenL/OYP/DniD3zrNJSni5U9zr0fOTUUfycJG0ADEdnJRNiuEFQNTBk/kwcif6Sg9eNnzBbHu7hA2uXYpzSV71oloCOQr5ebI7Ty55a+ceGZXyn8L0H7KAAJB2LK1nBY3JRLWkLE9o4Q1hE2EiZxCkBKW2QEEoYJy1trLd7oEO1I6O0j5gjBJx3jxZR28t/c993zLTz+tw7KExx//kccfP7Ghh/THQ6DOMTnl9dftwXtXHgr0T4IJXYyJYQcUKGu2lYSNqcZzoSAMbkFaeQk/v5bCjBXggrQWvZGIQowL9zkt6dLyVsY1GomfrTQ/pT99j7uEVO2Au2ccGuNCL8pgxrFPkH/YGiRisXboHJrd3QkWB6HMJmFECtyEyeuAzRrrW8qsjQDkMJuX6ETH7qfTr/sd+MJxaEjx9WqBjhvKe8XnEg6G8BBDwT9dFNpr8D3TktDmIPG93GgEsCFnXZj3lr5P78DxzMqaxFTX55wQdyYbWc/UyKe87H2Au5q8RdvcI4ht5yGxazPu/PcdLDzjR4LeBaBgWxFyvTm0oBNne69gi25iq72Fm33/QAkTogwlQntPLHb4aFZGlnNfbM0RlqGtNlvf86Nh8C8J0+qhxHrzZLCDSvGUAJZPSOzv3efQ5Y4d04iN9aAK7dun1csYHfaQ6ITugWaPha6IuIGV0QJwvarO30W9+4ERwAxVvW6fRnkwMyIFzk6D9/KrtrX0UvZMApOaPUD/W84lP3sDTbsnkDLVQq5szpxr3uZX9/PEhJM4r/w7vHYClEfQT/LYcOOvBCgkIgHWeb5n06jpJNqtOHvUGKzPitF+iaRdeThrK+YCSurCloBSsGYBn3/4BOe2mIYlQoQQP1kPUmHl0ogOFGJ8am2CLCt/n8NPOBbfW0NZ3uILfuZRWsjRPB77Bm8ExzDCczLfWBeTsLkj/fKysdRL2ZwwSUM9+JdE+DpjM/e/9xwqyuc9XqWTvxlyqfBY+C98EZ4AAl+dfy5/yV9DUhMPKmDlhOjKpXzUZgIrT/0b1uZMuh7bmV50witebvY9tN1pPVIfYb6+Sk4og5nhSQx2n0ovV78aL4VUmxaWevZkKPjET+mMEJUyPOnofUuGc+edx9CpUxoxMW5OPrljPYzQYY85VIQu0BMYp6p/210FEekDDACOAO4VkSGqOnkvx3hwIwL/bQ9HJ8Ej68Ej6BfdiOvsI2vyYCZPeYkhJWPwjA8RaRvEbYHL5UUsi4AU82nJBXR7ZyiZU/sx9aynKfKVkayZ5LOIZM2ilR7LEt7D/3wT4loVY31ZwOHfDiTlnHg867y0+roHoPx2+dd0zbycEnsDcWQANhtc01C1KZUNuIghgllh2Aq4yW+ynPCzMXz/+O2EpJQVfMxI7zkc7/2Yr7mR9YQpSl/ID7ecQvL6HvSb9xiNBvpwJ1i0K5uBZQ9DbBeDFw6iTYdMAE7wnMHk8CeERBmT8hTfNyln6lKBGSWsmuji3OKmuCTAxdldiJElHCuX7fKUTg9/xxVlo7CxCRNGsfkg9Crnx1xLR1f37eoujMzmZf9jHO0+kbMajabJqDgqFodIOKJ+117TgFbZvQP77k1hWcLZZ3ervaLD/iOa8P5Aszdd9gNGisggYD5wlarumOX3OGCiqqqIfAkMB3YSuiJyJXAlQOvWrfdiKAcBoeiqD8VhSHShy/qAWEhhmMOOuJXYSDvSL/Qh3xQDK+BRm16XXElKfibuxTbNRqfgseIIlhaxduwcwv4QvqKWnPbVPBr/KRYspd3mocQevgyKbST6it/21ezopJpNcWYei674llH2M3zgOZ2mdjaFsoICWQ5io0QYzDNM40HsvDL8CSV8/eZ/ic9LI0HbUsLybeaIL7mKjUw3x+ZWyhuvI5iWT9lhPwLDSejtRYPfk78iFW9ZCnkdx9F1+L8BGOk9jwJ3b67TEvxWC3waTSWZFcuXoRcoj5RwTEwiYuUSxmKWPs3x8q+dTunnofEEokv3xJOIjY0LN+nSfKe6V5SNIF9z+Cb8Ed3d2XTu1JPYTvX/S0o52Qf4EZ+QOMBJ+fi74BDSdH8BhqjqJhF5HWNC+GiHOvFUhXpsBTJ21VA0NdqLANnZ2YeWM2ZhGFb5TRawLSETjBBQ2BqBNAviXQSCRbTSgciK1UiFbXxzb1qJ624Xbf/dD85sAg/nwb/W4x3ehvNnfoV7UFP8BWH88YoVMUENzRZ1g60LASWn70pKLgrS7pVsNiT8wg/P/R9xmxrR/d1T8V9YwMmhcWyRufQN3saKFZ+yION52jc9m3aMoB0jmNv4BX6K/INwbJgtcRXcI09xhPzMnZTyIX+i0qfLwksybShhPYjNwrkJBJfn0Gl4Ov29t/Pu5YNBbFrJIJhWYty7zmvCuZ3bELYXsTzi5caISfwzw/6ehToLFx6KImDhwY2blHB7Np7wGa/f9QGnDL6Wrq7eAJzmuZj3g68RJEI71/Oc8atNn9gjadQnlcDaMOW/hQkeVsQ1CSdRoMZTRAH3flRbXAkWjc/bea27/cGUKWs4/fR3SU2N5ZtvLqFly6QD0u8fjkNI6M5T1cqFi2cCHXZRp5SqecEEfm9BGPkh6DzLOPCf0Aj+2gKe32xWf5hcQPj4WAqbrOHLhKsJUMC5//2YuBuLYH0A/GGkJIJeuwLOTYfPtxrhfV5jvIOagwixbS18rZRy3ULCwni4btk2VzGJCF9f+yiu727ii/GPgQsKu25A57fiCEnHLlV887LQCxbRpagF3aZ8Sml6KX57Kz53Kl3lYpa5P6akfA3j/LdTmprA9MgQJrlep01U4Ppykxl8w61kNMtm9aOL+drdklHtW7GlUzoiQrK2IYnWlNjrcE8LwYnzIaBEXlzL+I23E5ItHG51oXHkf6yWIkYFh2ETwGv7eLjkZ1zudaA2rTccizVlFpdechIDF2fzSvxk+rkH0cvdj4ykZXxLBWvCsRyeE8PRszyUx4XIe6MCDcEHFa+w9Ph52NikSCoPxY6lvev3sf7Zvfd+R35+BYWFfl5/fS533nlMQw/p94lF3b0X6rnbPeUNETlMRFzAacDcXdSZhbHpAhwGrN674R2kLCg3vrnR3Lnl7ly+feK/fH7dPeRP/onXkrJ5X06hU+FphKSCJcd8ic7ohYq9LfhBky1CH2yA9/MQv8L9awhHAtv8dC2vhc+TBL+WsS5rJhpdmLLJnCyGF7zM4nfnb3f1kpe0JpDvZ+PTpZR/lUDeZd0o3NycUCch/vgtxHh+I3DtbObwLFt1CSGrghPGJeIJKgkVyrkci+CCiIsBN1xOy/fa4322mE5P9GO+dCHk+p5LQyfzceA9bMIE7CJsV4gS3wY0YFbZLE7eTGlgExHxs0V+JeIN8IhnPIJ5Rkew8c1KpbH7eFptPhY5bi5BT5C89K3Y2Dzpr8oZkiY+XBKLAElRdx0NV3notdvYEyWMG6Gdx+Y4z9ADc+0PACee2Ja4OA9er4ujjmrV0MP5/VKp6dal1CN7o+k+ALyNGfJHwGwReVlVL69WZyrwiIg8DQyLlt8PRyZCj3gTIeYSYh+q4JiYSxg/53ZWdZpCODaAemxWBT5HCbNJfqYXVxF+NAP3VSai7Kf732FL7xWM9N2GWkowpYyf3Lcz2H6K0IZCrBY+LL8LHllHs80dTaAC4G9SSklyHutc3wIu3H4vTaZnctTlR+G+pQCCyVgRF8uOe5718ePpNe8Ses7ogwAxz5Wz4pnPibj9aAx0O2YiKy7PJv2vCcR0P4pMvmFCZCT+1HxsdxgRIRxXysUs4JvAaGYQZI5+TWvP6zQu70xR2QpObvI+OsaP/531xC9oSYtvu7Ju6Fw6rTkVT1YsbfmQxvGNWRCsoIf3Et4bEcdtuomYVsUcNesW8viVCm8Fbjwc5R6y7RS/RCN6UUZ6hVDW8T88dtwv9MsYxIqTV9Jz7nF83vcVTo9rii0h2riSqBagfMCx1WaxPZfm0oZGVuo+t3f77QMYPLgtjRr56NjRcSfbbxwq5gVVXYDxYKjO5TvUsUVkCHAS8LSqrtr7IR6ExIjJ5DUoCZ7ZhNgWIHhKY8iYkoX7Bi8RO4xdESZ+fSob0qYyNqYrPbL/RHxOFpvCPzMo5WnEtlh293/Z0Ho6G4Yuot20Qch1c/BsqMB/pY/YMztCBx/kFBNxhUEsQt1ctOvUHIZfwJQxrzLowZto+2h3LNsif8YMPPf1JjgthmUnPIdaYX7pOIbuTV5Dc23W9tlIzvTWpLeKoe/LL4LYFPRey1bvfJLt1hRYywl5yvj5sXFUZBQhPh9zrvsIW2282AQBlSDfWreQkphO+2eux9W0ArmkKe5LmhA5ahHZr7xA9itK49EJkAUncCHT3Yto6U7lbK6ni67GllRCeFmY0Iyk0E8ANJfW3BjzAGXkMInrsAlzHf9hQdwSrun8ABWUM9n/PtpNebvbk8SRwN3cQ5J7HR04la0soTHdcOGt8dLtSKmWcGf5aAo0l4djx9La1W6Pb4e/VFzE5ND/8BLDp4kLSbea1b5TDYgIRxzRYp/acKgDh4rQrSuqWgFM2F/tNyifFcC1K8ySOj3j0MYu8kvm0OPfI5jxrw8YOfdl4jMyyf/3F7R6qSOh+ABfffMcbbqdRnqwBx0mDcI9wgcu6Jh1PsWrtuDbuoEjTh2JlFQAikZs6JdIaHwm+Z/nkHBfIluHt6PVmIVYYaXLi8eTf1E5Wy8tJm3iJrwlsXz79zHENWrG0Eev4/I7X+bL/40h/8hiZl3RmbQSi3Xr07lxQEs2n51OsE0yywe9wNLhY0AVV9BL2/kXQbZNOC7A7Ds+pd1X16B2BPX4OTe2OWvXeknPLMKHUKG5eFyzcN3QEZ1SzLSXx7Lqp+9o9/lVtJ7+J4r9XlKBPpxHV4ZSzFrW8TWDCgvp/9BJlCbbfHr5EgrjwUsMw71/QkSYw3/ZyGxe5n5GaTlZ4UlRT4bqS9cLnVw9Ocl9PS6UtzmWIMWk0YUz+HCPLuU7wef5JvwRYUI87L9xr5KYTwl/gZ9yLIRFkTn7LHQdDhACuOvqVlh/b1K/rwmuA0V5NGtLxKziK1/2JKOgO6vO/oWmnQaQ1vdIElq3ps24nrhCHmIK4xl59G3YORVgKZ5SH3ZFCCoiWC9uIeurERC2kbBgu4333Xt/u5yP9Txcfi9xfbMo7d0UXBbhZC9qgYSF9Z7pzM58jncW/oXX119Hbp+VtH6yA1aOjbs8hgGPXIZ7weskl1q4bcHXLh0BEucFsCXIyoGvmuzqAioRQuvnIkELBIJF7Wn146UkrD6MUNji1Iev5Nr/nEWrUDRHgMCcv3wE5TZbK/7HYtcHVMTnsPD0h4m4I/hXhsmfWIEdUjbYa7k+byShx7P5x7U+bhxTyN0PlvPpJf/jjSm/8E7CNG6OeRiARrRnLYexkKMokXjmx5iXqM5WT0a6z6efaxCfJCzgnYQf8UksJawjoEWEqSBHZ2NvS2VWRbEWEtGdtwM0k1a4cRODjxZW5l7dDtfE3IULF5lWR/q6j9urNhwaAAuTW6QupQ6IyH9F5OS6dOuwp5yZBre1gLPS4O3OZtsPPSnrUkzrJzrjCnlQVew3OkTXQhNEXDRb2QN5MgcpjGCNXEQkazrB3wLY6Vm0zTibeTd+QTAuAC7hnP++QWlwE+HuU5m85QpWDHkbtcPknNWWcIIHFZustIFcHJzJ6avH03v15XR+bSBZH/QlEhMm7Asy94wP2Jj1LN6IjaKkBWxyR7SiaEAGq7s/j0oECVtI2EXrT3qTfd+ZeCpisIIuNs0dwT2DxvFI2kf8t2Q9M7fk0O354Qw/8694Iwm41EPqoub4u67m1xsWE8SDW+NIDGZiZdiENimlM4Osn7aEu8uvpNHSI0kpaE3GwkGI7SLkjvDJoAksLp5HF+m1LZChGxdyJtfjVRfNym8is+Q4PHg4y3sZT8S/yWsJ32znpZCs7WhhH4VE3Bz31gTW311G4WTj41uqJTxR8Tf6FTfhhJL2FGshACWsJ4c5KMoIzzk8EfcWd8eO4XbfkwA863+AwcVteS3wdJ1uh0tjbmFhUogPEmc7WdAOJVxAI6tupRZE5BigqarWmpFJ6rCO2gEhOztbZ86scbn4gwtVCCl4oxckJ0iw0w94InFobj+zmgFKxXPziHvID4OS0dc6IkEg1oLyCAycCw9lsviYyfjjCwhpKZ3P7EHilwkgUHyen6TXvLy96BaKO24mtqgFrf7XjT4PD6O0VR7N37kMaeTBtv+fvfOOkqpIH/ZTN3SYnhwYhoGBIeecQbIBUEHJCqigAoYV44qKKIrumlBMmBFFRZAkSZKI5DhkhgGGMDAwOXW8ob4/GlF/hjWtu+7Hc849p6dvddWdW9XvffutNxgoeTaixnZszWJW1ni0oE5JvVwKQhbXP7IPVWqE1CCaUFBMnWBMAasf6UpVuhC7qS8Zi1dzzYe9iS9NIBhh0uPz2jg8N1GS8hVIaGa0oe3MBrQdksShqguxpJ+NgVLybYN9rmW0I4HH7Wxq210pn6/jyzCwlCAH+z/Lzhar+DKnnOlvr8PhEzgO7uTtIZ8x96rZCEXwkGsqg9w3I84XkhNCMN9YyqO+wYTwEk0sW6OLfjTCTEoJIQidszj3uo9vwnRen/Q3FlgfIBDYWEQQyYvu2dS3qrHINQAENGIEHZn4vf7O2WfoWZ6OQQgVjW3RxXhE5A/Gvch/FiHEjp+rzvtLaF1JkdsH/DILq5hu/OR4QgidcKDYUuArKeXP2rguJrz5LeSFoFUG5IbglVowNgVZZKK/2BieOQ1+C+lWQYBzXEO8NxcSoSWHBbEuw9ZJVWB/WAeztkJt0Q87T0WJECiVjoBdAKpAyU3j3HUePHkplNU+h6EVcmzgJtpNvJrUtY1htw/ZyoPtMhGxGk99MAW97yGidAXFEwApSNQ1vhgynl4Lp1CctpvEo22wdBN/Yg4eKpNiDmFywuM85viIvNEQdUkKT2gl1DkZZPiHV/Pw6xvRVAcTPC9yaNxuTro/wCKABVRIm2wzSJL/UVZGzKY71Ykll0DvbAw9lmOp81B9Lq555V16+VUOpu0krksmwfrZFFSUErKCCKGy0fqKz8rfY4ZjFS7hAlWhqVITBYmLCOqqTX4ypFcIgVQkWoyCcAAKaAkK8633AVBQ0dDxiChS3m9CZsJy7KttbC3IqR+pIxgtYnELD5rU8IgonLjYZq7DJ7100a64WArofwkBuH7xfCYKIb6rFb55PrgLYCRwAHgGuFMIkSalfPmnOroodH8Ly4uhyAwnnn8mB3lrZUh3IWu4MLo5KBs6j/g516A4dRRbw7nEhDZBZBUnqISr5DoEwSoBgkoFnvw09FgFs8zGvK8ams/CXy4prpOI1BQqantBk5iRAWru6UDEJXVhawX02491lYed0xajJnaFgftpsLcfvogiqqYv4YDLg6lI1JYbWNWqI0hJ7MkmRJ2rg7OJyki2cVdwCP03jiW+onI4teIphSlPFJHftwai8g1sfKcf+vgq6IqDGK2CZ4IHaOj0UGqZnDD8aCh4hY9KFW34SLGxPQoOzUGvfeuxqwWpv+I+TsVm87dbeiKA3qXDeJq3CLgPsiBQhBQevggN5fOMRjjaOxFCCYc56/X40LWWrfZCejuHXbj1lrRYZy4jSUmhsdoq/KYCikuQcpeH0FkbV22NbkZfNpqrqKKk8XbEcuJLUyg4alA551KyuryDGV9MO+WH6UPcIoKFkRlsNdfSUbuURcaHTPTfioLCOMcj3OZ+5M9ZYxf596Pwa4Ruwc9o1i0IC+GzQogPgSnARaH7h3JJTHjX0yVgWFL4PUOCDt7KhSxaOJkR3isRDo3ynYc5mP0KecnHuDR3Oq7kcBSaHFGJ7LxF7HS9xfCkzQCo0QqnC45Q/PpWzu46Q+2VY1FQUIPna6/bgqopPTn7dhmbtCnUnN+OqrV70KbyBM5Yp+j8+XNU29UNieT0UD9mk60gIe50OoVVMqlpX0p6IuxVM2m1/Dvorw8AACAASURBVANkP8kx+yBtjasw1CCKVFEUi9NDNfyxR8iv/zXpZi9qCCe+QybG4nQuSXmJKf1vxilMhkmdRZ7LyAlm4pRnKLQcHA3F0flYO8rUEgpPV+Zo55nsjDkISAIOP5vjV9CrvBan5QkCrkfId46hpk8QsTkSmgsst4Wtqbxje3Fqs7CVZSzhUzrY0/nczOa4uZctxttIbCZELOMzYyaKlcVj2jTqe5rhrq0gHILX9UXstbaz0VxJjsymakw6erLF1BaTWK5tRZZLivVlPBjR6wfTO02J4WXHJbRhGSLwMOb5DNZrzSXcxkWh+z/DHxeRdgSoef51a+DEzzW+KHR/C+kuONkGWWCEX/ttGHeEIy/sYXvMNFqJu1AjnQgEJa3PsKvDQvre/CiuF1PBqSBHVebwR6+jX5ZI91fvp7zNKSI7VMXIs4irVoXt0Us513UHgdhcQKGsyjGqbe9JtFWH2GpNWO0eR4VyhqKBh0iYVBWldQeit6RQr6gvQcMCxSZQVB+FLSSHgjR+9BIi2z5Iwg2dEKgk7bUp3RjiVEY5j9z6KpnqUe4d0QcpbOoURdGjZivOtFqMrYY45nuDm1rOoPiaerhCybT1XkabrJ5U+LMZlNGeo+M9ZJsKupmDiuQK9UEazbsBuwy6bBvNxtuG40zOxFkuCUqBokpOy2wkEB94mTjnbTyyQicUs5Yd5t/I1AwOqk8xVfaiDbWpIXsw4vNGjGx/LT5HCF2JZJT2Tz4xp3KXuYAY410E0L+gK5rm5o7oOxmrPITthYniFo7Kg2hBjTnWDmqOrssWexlShPcxPjJe50G+n3CnAptnqcDGyQZ60EaUna8HJ+iq9/nTl9pF/o18s5H2+3kHeFcIMZSw5+/An2t8Uej+VmI0cKthX91SCxYXUWt2ElXaPoJzdVcUoSKRFIj9ICB5aTr2MyGEqWPICtbfNA2pSjrcPZHU67zINjbOVA1nWQwtzHGs0MdyuvkShABbSqptuZWo03WwQxAxMRF/VAEYFhErdOSaDNSXGhDX10nB/AqKI/dzvN1cbKFQJD2k7kjj0MtZJCpdEIqCt4pJ/IocHLkl+OJOkXCVjje+iByRjVOvQ071eUjdAgGWK4BV4MUb3IXmbIhuOHiz7xM4C4MU1z1L8/F3s98WFGETK2JppwynXEqE1JBIyi2bbOkl3aWhm23YKTdc8HiUKDTnPdSrPqCaP5Nq0qZ+iUJe4nRCsgPrRX+2cSXVHZsJ6F6kYmJhcKNyPT3LBzLEeT22AwwzHjXaRwiDf1oz6PrScDz5cQxofBdPXTWanvsG41icwhnh5d4bn+fh5JEIBN21vj+Y1ggE6Sjk4MWFn4ERTTjgj6Oqks5N5ffhP2niqq3+7iTmv4bgcZNQno2nmY7ivGhT/sMQ4teYF34SKWU5MOiXtr/oMvZ7kJyfOAVquVFNDWduBMIOp0k0qCC3bDOtl40m684tzFF6s/foy8wVfTHVADYG3nUHIcuPvbSUQLmPOUlXcVrdQDPfNKzz4skGNo0dztr7+xC59hDdO9+AJyOFnsPvJHF7GmKPD3tRIWoU7B53D1/fOAzL7QcJNT7uhGtvbRxPFHNabCBX7GDr+nwiM0tw5tvUezKdy6oO5FPHFtLzGnHvSy9Qe35XkoobUulIfbreNI7THg83P1jO7iEPs2vAOIRlk3NzPUqv7knlXVeSb5/CIkSZLOHZwAOErsunvNEBNl31FK/EfsVKfwmHDclBmYF9IYsZtDt1OY3lTCxXPlLYaEgibBtpJOEytxNhrsVhrmVO+5FYwkS1de4STxNDNDWL4pgy/2VMkUBx6EZAoOBHCIsjnaYRdBXR9cC1tFO7M/zAfQhTQRrQM2sQO6JLWRS5h6kRs38wpQqCXSQzmwhWc5rb1eW8HbmMh0pepmCqQf77PgrnBv6sFUbotMW5N30ULwiQ//4fWDPmIt/adH/J8QdyUdP9PaiEAyT2eeGkP5xeMFdhiX0zVfQOBO0y+mgzEJ0UgoVH2RH6hC1NX6ba9lbEeOOo2/Qmap5tB3lnEKOyOHdnXaJ61KHFrW0odRj8Y3sZ9Vwujho+epu1abRgIqXdG7O52Sqm1N7AE55OpEWYKJqLcnckRVN8xF7ZiROXrAxfnwDTbYAUVF7Zlg/Gv838SsNY1q0RKKcx3SGUmrFoOIjU4mlwfAVV3JE4AqdQ/a/yccrfuPOZy8ivpCO0FA7FTKVHxkhyR9UDIRAIWq58nBFjHXwgpyGRbDBWsC5hGbWvbcoiRzsSgxoKQfx4GSxuZa58m2RSGbj/CjyHruKZarOR0sLUE2lpx/OaGmCt73OqsgiJE2FLpAhXbLAwOOWDspMG5cuCVIt2Exv1NMcjO+HxbcNhZ1PD2ZkzbT7DjCyga9Z0Zkauwd/VJO+YD6FCqHkpcSL5B8nQv0sUCpeTwnSi2YVgFJLQmXBwhQxB8PiPB1r8OzCL7XDwSgjMwp+rW3+RX803wRF/MheF7u9AaAI0gewcDSfaQoUFURodlCR2imm0Mu8C53nXsQG1GfbcXLx3KcTUr4HYUg7umHCetpgIrFHHEKZGy3eG4cox8Zgqj9w6mTXvbiTVtYEQRWQMv4emc56g2qk+WEzmkRef40yXYrSUGvTZ2ACkIHl1H7jksfNRiwpV9l/FqdYRnH7iEJGVDnOjvQNn9T6wtgnlO/aR7RHEvF/M01dLZvS0GbrZS5ue93GFYx6FRfXJS1XRhKBeoIyBUz/GUe6mpGo+0WeSUBBQ7GLElCeI7VaNkd1vxi09ZMhNjLZfoNQxHF3mEGUsQZN5LJQzaW1dwpR5c7FzBE+OviIcQSbgYb0t59z/oFZ5cwRht7rmm5vSY/7zvPHQEHzRuSBgtmsyEafb0iWlEc37JZIuGpOBh9OeGTQMvcFAZTZSgLu+TkLj8C6Ju66GZ3KAft7mlIpCbvLfw73up783l4V2HguMmTRUW9JB68Hlr6xj3T+3oQ5Kx3j+MsY0jqRii4FRYBN/9R+bxPzo0SJuvHEhCQlu3n+/PzExrgvn3A00IprqhE5bxPd3/UwvF/nV/DrvhT902Iv8WqQEf1jbKZZH2bT8Xuz49VB/BzLLT5ysTU9jGnFqrQs1tVBAH1qNWGoiIrWwi5kukIrAruYk77qaCB0i+9ZCUVSkkLT+pDVDRvVARwEhsfUgX7V/m4eGDSbSH8Mbb23iqsxnyLdKCIgKhAbBakdRAzoqLlL9D9B2cg/qbY1k5+WTERUG6Z8nkbPmOGb1CHK0RkQdqImapXL1bHArJWS3mMPDZY2YNrUps15z8+Q8J48YZ6mffTuiQkWYCjG5Sdw7tj0mZtj2YUPfHTdxyNpN85CHkUZ3Otk1QAgKXBMojXgbBYUgAXaqGym68QifTGyBXunIhTzBJY5hREuFAbIOLWyBGw/Zia9w7/PpZCUsp1XGZXiIIkKYzOnRl03DnyE38QQzaEcdYz6JgWexfC+wKVjC7mA5BUZ9vhv4s5P1+EQ5BiE+M977wZSO9l7B1MBDjPVeyf5gBl+P/wpyvFivHyQj6xCKS1D5dg/VJkXhrv/HZkkZP/4LNmw4ydKlWbz22rbvnROqIHGImyr3ROKq+ft1JCklTz+9nkGDPuXQoYLf3d9fmm/8dP9k88JFoftrCdrQZjd4NiHHHmGdfIi05+uiBtXwhtqcfIQNQkouSFwhwkeyMyywA3a4nRnW6EQ9NylTokltFyK4R5DXtzry/GfTPmlEt9FjkUAAJ7OTNnI29iSdj/ehanFtBAr9dtzKir+1J3jlHdRp0YC2E4dR+et65B3fg04BCeIMAonl9FFW9QDy6wTGHRnAvKTt6BbsS7UZOjZIQEazvvsuAucaIqTAbboYusVBtxdsMhN24UwKCxtPa4Vrqtfk2SsKidqSS+zKk+yssYynzbsxMbCxWSNfonrFFVTz3cPt3Ik8b8u1MCm2C3i/Ioc1gRKqCQcuNGKMz1hecg2TQll8aGik2yaZ9Vz4PArIeIbEzWJFVBZ/dz2PJQ0a+p7hXFFj+pRGkxZ4jXahlahYbDNL+TJYxFOhB5kRfPHCtLVWuxApolHRGOYY+4NpLZR5GBgIFMqVYlLTIlA8AtVlUyf55+uqSil52n8Pvcsb8EXosx+cP3WqlOrVX8TjeYrly78tI//pp/upXv1FsrIKcbs1dF2lRo3YX7MafzUrVhxlypR1zJ17kIEDP/23jvVfjwB0+5cdfyAXhe6vZa8XDvqQMSr0jqOTOYmcoYewnBY4BaJXXDhibV4h2N8KXikl5a5zBM8VhqtF3FgZnjwJz5yieFcuFbfnwPVZxEw7QjAtCsvNhcTlVRa14KPCMkr2t8CT7+Ktgc9y46SeSM2PofkpbbAWR5LNzrhM8p5cSLPnr6DD3UOwa6zmJvkYbUoPICwnltNPcY1dANiqzdKWT5BRzeLTNgZ+J5iKxlcRl3Ow4XLyYk5+mzi9LJXUolrIMQVUedRNdD+V42YFWZ6XuPmxa1jRYBUJ7+exU/l+SLnDPkakuRivXRFeaDJ8H/5eNhL7/CbhSRlikutN7vc1Y1WhSp7pJoBCDJIE7iY+mEttcwVz0mpx9sgRLvloMFccvhSnw80tDjiHlxMyi57WKV6yJIqECEVhWGQCpY5p5Nhbecg7mqvLm9BfH8mm6DzudD1GhSxjgm8UD/hGUmIX8VLEp7RWL+EG53jaad34evvVjHp7HY/v/pjEmP9bAvD77LN28EnoDY7Zh/i7f+QPzn/yyT5yc8vx+QwmT/7qwvtjxy7m5MlSTp0q5c472/HxxwMYOvSnbc1/BN+UfVdVgdv9H8hr+N+EABT5y44/kIs23V9LgwiopMP1SdArjngZS6UberO6+0w6O57CVSkSWRRCOea/kI3QxuaQmEOdM5ejtz4Y/j3dxINxdxyLat5Kq49nUOPD4whLIpFsv+FmSicc4JpOk4k+VonpD8yg/rp6jH5kCO2aNGLi1GeZ8vfHiS+LoLxqNqc6ziYuqwPlqZl8/vEULr1kKmkHU4je2ZBP2j9CaXQ0DY0lVPedoN6Sezjb4Esqt9jCXPE4w8b5sRE4DJCqSQe5jMZJOsvvG8NtH68gtM9BbuxpjlU6yR3FrzLc0461oU9YbW9GrbOFHC3EhOmTqLvxc0r1CvTgYRTpCz9rJAhbY4m/EAcCS0ikhFK9GAjfHhV4oKKACJ4hWMnkda0jzbXr2KI4GCGLsLxdWa542SbgYfMuph1Yww3Zr3Bf/Tp8V/9oZGv0skO0twWmy0O8oqMKk+lGPz4zzwLwduhZhjnHESPimB6YwufGh0jAI6KY5H6VWZHhsGBpS6rH1GHskP5kiwxOcycHMWhwPvlqrn2KMd4rCeDnUdcrfBJ6AxMDF25SlDQWhD6grtr4Qs23Ll2qc1eH9tzWpi1Fug9pSoQmaNgwiYyM8LWNG9ea6tW/1XLXrj3O3Xd/Qfv2qbzySh9U9Y/Rj7p0qc4771zNrl253HXXz5e0//8C9c/PPXNR6P5aPCocbAVFRvjuScBn0b3qK6g4wmGs8U7k+FTEjYdhnw8xrSZKZ4HIDpdAF14bc18hm66ZS6F1jMw+L1H95SvBAumG4tp7CUX5mLv7MY4YFVSNMbnrjptIPhNF4olOfHjjfNaPOMGQnRYb/zaMjq98hLu4CqbTx5r7+1NyXRXU/ZX5snYDCtV4TOGk4P1/0OvjQk7e9wyFffZSWWqYsgUBReA0LMauOcOA3Qkc7u9gXt3b6aiMIfH6aOpXHMRhdUUQJDX7DItdM9lS+4uwD6+mINFJKmvCjk7ViTKXouJDopNY2oZrdvZkZqfnMFSTwPnSkQjrvAZ9PsgOQVJ5EeVRgDBQZT5LnT2JM/czWOvIDeq94fsuwR0MF4Z8s+dDHJPGhSmR6CjR8yHwKVP1vpxUJJt5AKTghHXuQjsbm1gRrsQQKWJQUAGIIhZb2iwwZhK0AwxgFKoQVBatWO94iQU0YyKVOEMykSh8EJxGlr0PG5t7fcMoowQFB9Uc1+G0zjLJPxaQzI3cRh21Ee3aVaVyh2iwIEnxEDxl4UrXWL58OEuXZtGsWfL3BC7A8OHzOH26nKysQvr3r8/ll9f+w5bw0KGN/+0a9V8C8cdrsb+Ei0L313I2CI12QokF8+ojzhqkv5cCy3SIUMICRQjkzgpYUoSosGHMEfT9kZzusJ/4vhLHVzabn/qIQ9papG6R3X0WKz4roO7SDuTdcIxQlI8ms58gdefVKPf1JShy2PTcLA6NWsuVl0yiKKGEk0omtiIRtkJkXi2EVMDWafHBcySeqYuMk6Rk9cQVp1L3eD4v31GOI6Rhbfg708tuQOiSXt5PWeYZjsohlrW9mY3tNK6PjqHAvJW1ipeaywUvHT3FA9cb3PzlY1y1YzQAL/S9ky8bfwZo9Nr9JuOXXQ0CJl9+NVub76XF8U7Y9hhmdhiHpZkoUpBspbIvZhVacCLR5ly+SQptIzlWqSpdDl/F9pqnyXdOJCb0MamBp5ijXfvtfRdwj6uIyFZvEqjz1Xkf6W9OmtxqbyDRkcLdVgGDxShSjLqUiTzmhcYC5QAM12+7kHpxtPN+IkQkljS53nkHs0Kv8lzgwXAItXqCe/Wn8MjKqIRIlNk4Qm9yn7mfe12TaKy2wYErnJtYxFImSwkhWKd1QepVqOJdQgQecuxs6qiNAHDX0whkmQiHQE8OC/vISAeDBzf60WVWvXosRUV+bFuSmvqfrQZsWTaZmYXUqBFLRMT/mEnioqb7F+DB41Bkhb/vQzORXWNhqxdeyEEOTsIs9qG1jYe2UTAxDfn4SWRtF4rUWOa6ET4Jd6PgJNJbhaBWyiXiSeK61KbwssNk6+vpabyMY2dXhK2SfLArJxJnYbkNChrlMHrR3ZTXN3g34g7anDRJyejNiXazSds6kNX199P6aNsLl+opqM0bJ+8nFHkIRXkRW2j43AHeqTiLx3JjBj+iljkVqUhQoAw4Q312qCOxhMKmHj72rG1HQkUlUgtr4TDcWIpJYVQuAAKV/lkJuEwFS7FIMm+h2dFOTJ7bFIHknT6DWFL/XaRqUlucZlVRCx7XxrEwnMGRNOCwArHGg5TXe46E4KPEBR/Ba+8giORjWUSZ+12ijcWkmKu4vWokE2t05nF5KX1DzamQIAWApFBJ5LjWmx2hfVxNgAi7Jq+Zb5Cm1CHVqo1fKecm130X7o0udEY6//btvB7VGbP7KdY0+ZSCGrlYIsRO7VV0mnHSakpy4Ha+xMdR3y5WRmVRRUkjgJ+aoj6TQv/kM6Uq5VpPqmBQQ6lLE7UNLQI9ePeDXTRokEj7G6pi5NpoCQrKL9gNX7LkOmbP3kezZpVp3LjS71qyv5c+fT7i669PkJTk4cCB2/B4fl1JpP9aBKD/eT7X33BR6P5a6kZ8+zooYXI1CFp4s04RUTkVvaYbaUnQwBwZhxIvODfwOLu0l8Pa2XnTnC2D+J35dKiYSG13PwpdB9jgeBQbk3hZD6uJin+vTa2vb8LXdD/FUSdZFjpBhx4B2gkn7XmOV28ZzEj5OQ45jwMd3+cl5yY6ZF7JIwtmEtAFH7YzeMhr4spvyS0Lx9NyTSuWDlxFghP8JSZFkWdBgC3dnPZ8jKE2YLnYioZBl+BmTpoNCGpptDlxK290fYwYXyWKI5zsTduBIOwt9nK33byS1RYcfpY2MXl8ZwkOCxRbIS23Omp9gRThDS4NP0POLaJJkqSVDelAMwcIKoj1j+WEAqpdjI6GAeRHTMYUSfj0rti++8iLeJYBqEy1Ehml92Kab9UFZdcWScSFprMw+AoFSk+KHTez33oPFR+mqEKFdiUTSl7j9WNP4qyuoiepF6Yxy3uATh8MRjU1LttzHdGTLDSHkx48Rw+gPVsYCdgoOAn7yjbXvrWHvuaeSmXK2YzBQOMIJdq1DHSMZnDvz1i//iQAGzaMokWLb8v4BAIm99zzBWfOlDNtWm/S0mK+t8xiY12MGfPL08UGAiaffXaAWrXiad++6i/+3L9CSsnKlUeREgoKfBw+XPi9/+MvzV/JvCCEiCGss6mAFxgipQz9nzYacOz8AXCnlHLv77jW/w7urQITT4Qljg4yRkPcmIwj3x0OB9YEhuXFSy5RhUkcuH4Fm1xTsAiiVjixIoMXujL1AFtjnqWRMYLd2luEKANgl/kGXa99CqvIInQqisuC71PozOcjqw0uoaILi1pyL1vkNajnpU6iUoXxG59mbv1pLHmiM2vV/gzb0I42S6eTUWMdOwZ9zMZ2exjqSSJeSUBxaLxfYhFSwHLfQ0BriRQqe2R3NhT3o4l5kJBw0P3u9RyIH4U7mMzQWzKocPWjib83QWsRGipXJnxF2l2PYtoqVwvB9GYJ1M6egTMQje7sSkJZCiLmOI9ZNuXAqJQjBMO3jvkhHQk4Mcg4/zD6JqOXRKOS/wE0+xzlen9CansUy0GLkzoLE74il7Xfm5ZmoY2cslejEGSDvZJC2Qxd70+c8TEnIhdji1jmqjp3f+Ej0adQ5UEPWpTKWTuHGyt6MUNmnM+866QgM8jQu9+nbt0Epk3rTTNHO552v8tua+v3tePzCASTiOa4lUU/X2+CBPjcmMWpo/fh95t4PDonTpR+T1hNn7GTd2fuxvAbBIMWy5Zd/7uW5YgR81i6NOyOtnr1yD9M8AohuP32Nrz66jZatvzPa91/OP8B88Jv3RK9HnhBSnkZcJYfL7HeFPhYStnt/PHXF7gAThW5tCFyUCL8M51i97GwzfbtMkTAxpYG6x2PMlf0ZtvhOURNuoZqGwagBhzUmteOlv8YhFYe1pYVw0GCUR8ZsEiwGlwY4qxvN6tPP0xWcA9D7q9HUXQ+cWuq8dyL64nMaQi2IHndEB6f35929p3UOHotjd9+ko7bbiIvbinj9RXMF2PJMRPB1mh4sgMx3kogoZLqxKEoOHDw0KoXuH/Ru1zjWosugghpI2QZbczdROFDt/1EO8eSHBhFwNmM8ogBIAyqaZdxNHIHmVEZ3BXzOjMcbrp5Qqx2xJDtqcmoQVcxZFQnvuh2OxUxBZzWbPrq0EkPmzACAgLAipgouiqXUyEI/9QTYQF2acVAFGniMb/EaR8gMfg03QOv8fZ7KjPedjFoYQ6cr3nmOv+dGWPk84b/EMhoTKU65fq1pOKmtzYERAJSOLAUmzItHFKb98ZGgpkvkWdl4nWV8tjg61jXcAGVRkVw060L+fLL43zwwR5mz84A/wz62DYTXM+SqlTnww/30LfvR6xadV6fkH6wThCQ4dwIEokfHzNm9KNJk0oMGtSQK6+se2F+P8PHfbekEjw1DLVBHElJ3/n19Bs5cKAAny/8wDp6tOh39/ddXn65D6HQRL7+ehS6rv7rD/xV+Cu5jEkpX/vOn0lA3o80aw9cKYToTriUxRgp5c87PP4FkKaEbnHQLQ6pgF5ogVIGh/3QaAfrTs3liFiEUBRUfxxCKjRceT81FseR8GVV5m2aiDwf+uooS6T5My+Se9ksdLGTesY4zjRaQ3lqJhUJR7DuWIw7FCTz8Bba/n03rQ5WpsaqRwk0qIMV40LYkvgaY/EfNqko97G4lUFmbEI4sEKovNcxjR4nTlMv36Tm8TqYaV6S9lxPSZuFJGZ2oGXGEHy6oEK5nzHmMBb5I9Ht9UzQYnjcCPCpsMiTG/GYNlW9Rzke/TUSi0N2BtUrJuDVe3DO9RzPqz5MATYVFLrHYokUIu05ZMtMBigai8MmY4rPa+UeBHXK4pm9LYmjTQ+iucCntkXg4kBFFp+XN+ZMySn2p245v1kmKZQnaL1fxaMrtDt0GW16xpHtKeJRA5aXt+X6iE8Ris2nIR+3VYzFSn4Qr7madURTxwfXWzDBP5tQzw7kzZ1LYr9h6J4CGpc355rAaDbU+IK9e4Ic/2QDiYlunM6wcOnQ9D3ssneRElZv2co7H3Vk4cJDBIM2a9ZkU156M1ppU5Cl1Hffwt9dz7POXMoY50O0uKQ6e3aPBduE77h8vYAXSxUoMQ56vdaT11vVwTAsVFVB+Y3Zy9566ypuueVzGjZMZMCAhj84f/JkKV5viAYNkn5T/5r2P+rS/1fbSBNCdADipJSbf+T0NqCXlDJXCDET6AMs+j+fvxW4FSAtLe33XMqfh/3915FxVZErYhBLizly4xbOqtup4mtNnYpBuA9citAhon4E1fo/QOnggyhoSCFQpEaCqy6+yRtY73gSKQPUymyGpvnDfQtQXH4u0aI5l72CiMJxhJJcxG/2Ince49ygdMx4F959SxFBD4qjLk0jvkYonUCGvyBB3UZI8OSnM3HZLGw9gBbyoH7+EBLJnLZrOVupMt0+fZSq9d7ln1aI3JXr2Vb5IAezu7HlgRYIM5xRS5fZYJehSBvFeBuBTaSxDFUmYCGxCecjCCm18Wt1iQwqVAibeYqPoISHLR236wUitR68d24hi+/eSfKrC1EUm5BI5bRnFiqSh5jKStfj2EhUU8NSTRymi0Of1ebZDet5sFM3LGnzqgigBB0o3kQaLX8Qrh6BcHhpaEsKEu7Dff7xHqCcZPNrHgjmoAo47j3BO7uWcMXiq+l1/evY3lNc9/oikg9fz/ilK7DNs/TtVYeFDw3Fk+wgJvJebCuALQUZO7Yzd27chfBi6VQwzS1o0gcEIfARl4dOkbqvNw3aVQWjBF7ohCw8xnJtFFM2tuIf/+jFDZ0T2EEpKoI79lbhw5f3cufCpcTEONmy5RZq1oz71cuyY8dq7N9/24+e+/rrE1x++YcAjB/fnlmz9qIosGzZcOrXT/zVY/3P8I2m+yfzm4WuECKecEmKAT/RZI+U8hsD5nagzv9tcL7G0JsQLkz5W6/lT0UFvqOvCwS0iUa29LDG2R1bNSn35NDAGsrax3tgWxYNll9Bi9GDyZg+iyiq0dK4E1XoVNcuZZf6StiOKSCrwV6iy/opPQAAIABJREFUSSPSrEqFmoNAUF9Up231G8gb2igc0VWawbFOr1Fr/rUUtvSQnrSc0q8eB8tNk7212Nz6KiZZ3TmoVaEmBs0O34ZAoJlu8twO7hoZQgofL33kIt6bT7/lHXCaDRAZV1HkOYtaWpM2ZdVZ2/p9Gjg8bDBLsFGwRS3q583GcD+LRA1nAMOPx3gbh3DjELXIVifhsPOINpbhdwwn1dxCocxCCJivN2W2dhtCCDpXrk/yDW8BCxCahSKSACcmgiXOKznj7E1M6H2i7XlE2DoShRpX5dMxI4ac0lJCLbOYlFOJ5j4/X55J5MEQXOGPR6ghfPuvx91mDn68KMBAT1UuFZM5aT5K9UA+nfsPp6Qkh9fWJZPdpyPG9vtwGC4qgiEsy8Q0BH3ddahbnoRRYlIQXRlXO51tGVV45tWOCAGxTRIpuSIVObw2b7pi+JuvEoGTTclZ/zwdJr2K3zBo3LgSm99MgrJchLRpVfYxGzZUYtCgOeTm3ktfXPjm+HEct3l4w3YMw6akJMDcuft54IHOP7n8vN4Qc+YcoF69BDp0qHbh/ZUrj3LwYAEjRzYjNvb7iXHWrj1OMGhh25L33svg7NkKhIAXXtjEm2/+y4rh/7sI4D/gAfdbN9IcwBxggpTyp0pTfCCEmALsI5xL66nfdon/ZfyfX39BpRzNdqLMLyGicyz+pFIEggPax/jUPFDgYOvPOZ7+FcVROSDha30CIwLb8Vn5HJPLcXqTCHkKqb5hKM5gLF0Gd+DLN2ZydMAqgqIQs0Ai9XDJnsI2FodHrOfQjeuIyWlC/PR3wXKCEkLT0vC8/wxZo/shVJPjUmF7gxa03dcFgGmXBtla0wKpMPUyP24W0OVQPwAsKdDjj4A3GVAIOSuoN+t5xl36DquSBJ9rr1KNAbikF4nAr7QjwloPAkJ2ANvOIlEOwjSjOBm1FRWNElnK+pBNAklM9t+NZYGmgYkkcHlvyj5uiz5Ao8z9KCo2aaETHNcbYysaAaUproJ1iNh83JZFscfHtEf6c/a+PiRdthJZuYRMCaLFOSYEh9PoxePonlKUqEpUaf85Ry0vMYpGVTWBNlYTcqPe5aAjG6/vHDYWDqeNM/ISIi7ZwJHjtWjULUSy7zhn19ZAFxrSliiKTVJsBZ6IEKqqMuy6rgghKJrQlE9TBArgIwoZf5hzL1SQdboAb0UIv2mybdsZZFpvhOrAVk3mH62PriskJ4f9hFNRqajtoCgjQLeaNcjIPYtpSnbvPsfkyV+xZk02Tz7Zg86dv/8LcMiQuXz5ZTZSwtq1N7J8+RHWrj3Opk05SClZuDCT1avDocjHjhXTpct7lJQEiItzEQiYjBzZlFde2YaUkq5da/w7vyl/Df4Aq8mvdRr4rZruaKAl8LAQ4mHgS0CXUn63gNRk4CPCYmqRlHLVbxzrv4YsFrJVPEt15XISqIOKk4pAHnaJTo0aTWgafRvBUDGVnqhE7i0VnKm7FSWk0OWOUey9YwVa0AMSDIePI+8fxHO0LtWbjyJjyASafPYYVTL6olgaBV1zic+7mqOsQqoW+5u9QOeNswlaXo72fANbt0CRxOQ04kzjL0nM6oDiKiTxphnEi6nUzW3BwarbsIXk3gFr+Ft6BFVTXkZW6oAqBqKaLjbUe44IlvDo4BH02juEFc0+4ly1QpofaEAV1UG/z5/GYbqIOXM5k2/3IaMhqNbCae5BSEkdeYLrZCq7Q4WcLGrMqcqZGASxlXgkToKKE0O6OGVvZ7mcQx/XSHo5jtPPjmKWGqCuPIc6UGFv5Eyk0NGlwa0V/XgobjNIF8IyMJ/uQPI/FpFk6WRLiRnlJXbKEoJno9ESBeK8PU5z+Ei9uwDzjMnOSnUwjEL+aUG+WoOTgTFs8vblOk9/HEou13/akKx50fSc8BlFjj3UlAq1/hagyHkJL6dsY/imqkxcs5yJPbqhRp1iSN3ZICLo2qMvXfuFy/WUYhNPGR4E44nkiSe+InNJEbe0bsUl6dVZf/okDz7YCRGbCo9moZSfpf5+jacuz2XEiKYX1lNEIx29skLrWilE7NLx+QxWrcpm4cJMvF6Dgde+w9kD70HEIxBxKwCHDxfi84U9IubOPcBrr23D6zVQFLBtOH267EL/M2fuJje3AtuWdOxYjRUrRgAwZEhjhOB/x/Xrt/JNHPrv5xungR9WOv2xYb+b/u4/SevWreX27dv/dcP/EBZB3qY+Nub5mlkaCipNMu6nqfMG3LUcF9odOraUyBndCVqriF9n4g41xxd3Fm/7xoBg74BHafLZZFTTicRmxRPt6Pb0Fzj9cdhYFKftJrIwjfy6mzjV4y3qTr+KhNJbMNwVnG22Ar/Lzyd9MmgpVqObKro/mpgztbimWioro55ib9YqZsQNJqBblOg3kOTqxYQTM2nwxV3sqJnLsy2XoilzkaoVfgiIBE5FLsFSEnCZh7hr9ReM/nISmq1T6LF5YFCQNQ1t0orXESVvwqWaLLMECZaBicJQXeWgYmOf9ygockwE6waGbS1jbeuOhAjiEdXYGbWB9LIW1BMpLAgcAgy6e+7hkOs6hvg/5JAxjRNaHcq1HjS2N9K3JIpb1R2s8cVxauu9tDzanTeS3mTuP6KJ2mBhRkC0doQF5UtoovTjSW0NHyvFvGDApRIMnDzqeYD3nVdQpKbglBbTysfwklyLgY0HWB/SkBHjcUc+C8GlzJ31MtknfNw6cjdrdz5MrVo12LG9FPfGDjRPTqHK4Eg8LXUOHy6kcuVIHn/8K156aQu2LUmMiGB476ZMnXv5z64lv98geNii9JMQQoB7qEqHa9/h+PESJkzozPPPb8IwLOrWzGf/168AKiSFQChs2HCSceOW0LRpMsOHN2HAgDkEgwaVKkVSs2YcL754Ba1bVwHCZoU+fWYB8Mwzl3LHHW1/5qr+WgghdvxMdd5fROtmQm5f/gvHq8JPjieEuA24nbD77L90GrgYHPELEWg4iCIoS5HYSMywq27DAE5bQSDO5xRQ8JTWQKoGgWg/Mq0HRdWiQKSgmuHHavNXxmJUKQUthtKq+5GaSfDW7TCjJXpZLLGnG3Gu4Zek7rqK9t0Hcy6vDCNCoIciqbZtAHcN87PV7kAzfRWK04/l8IOrlJccA/kwtyvlSVtxGR4EfmKNWZzQu9N85itEV8TT7aSX5VVe5WBq2E5iCyd+pQO2qIQUTvxaC0au7Uhm5V3kJGYxr+0Cbl/+HOWx11EWcZD2h66mitvGWW3x+V9mkhhsLGwsEY9ul5LifY6JnzUl0hfHiqYm0iEpwU9NYws7ggVAAX4RTdfYJWRq6fQytqKYFspbt1Nl4Dzcld7lsoh4EpylDLTeoUtpOUN3DUK3VSYVP8W2ZY2ISprDuWAyLwVvp4mtkikW8qliYgvwinCCN4mgjEgsEY2FTviRGBlOPinAK+EV51CejRjDagwaO/sw8Nq3IbQcKQVtmx8iMvl27hw8h1f7JuO0NQoXBLjluUUsXJhJvMeFEx3bDisuBT4fl42u+SOr51vWrz/JZZd9wNTLr+CK2nXC8TLHFLKy7sS2Jaqq0KNHOls2Z3HDVTcCEaBWAaFgGBYNGyaxZ8+4C/29+eaV7N+fz113tSM5OfJ7Y3XrVoMDB27H6w3RqNGf7197/HgJY8cupnLlSF57re9/Xwjxr9N0E4UQ39UK3zy/JwW/wGngu1wUur8QBZUBLCHbWo4mIziiLkS3o2gp70AqNhKJRYhcNnNYrKB8ZDZFNTfT5Z/NiSiLwdIDHO06nWpbr6W42kJaP3gJc/feTkn6IXTFTXpqR3I1P4qtYaohnN4EnPWASA33VZEYX4Y40vUt8hquJdPzIrmOZNbKa+lgzyNSGARcAXYHbqbCXQYCAroXIQERoLJvLEXujXh8USAFRa6r8SkJOM8HGFQ4rqPx6XL2VHVQPTCXJwacIaPmbCztBNhuNjR8jaDjGFIxyUhfS731u3m/wW6uDJzhhKrR2hNDnB3JNDGT2NAHtMyug1/pzrT0kxzf9jJaWjlt31nLnAkDiQUs4GNHT46o6QRFBF9otTFfdcETu4h5bQj3b59PjCfIAsayTY3kdHw5A1SBoUpOx3mxK+fS1Xc7E/euonj5+4T6D8JTbT2WqEROxIuMkjZj/OvwatXYJCrxTP4/yHUlcVpP4Zrgal7fnEbwkpOc5UHuj70TB7CSII3R2bRnJOnxq1AUk6S4GRjlizE94wHwGiFiazpZ8Nwh4nQ3y4aNRBOCv69YyW7fOVq3TmHixC+JiXHRsWO1H11HM2fuxu83+WT3PnrWqonDoeJppiOEQD0f6dK9ezrdu6eDtQGMzeQWdmZ0nw9ZtuwoAHXqxJOZeQdCCK6/vumPjgOQl1fBggWHaNYsmUY/nuLh38rtty9hxYqjOBwqzZtXZvz4/8KsZr/cplvwM5r1v3Qa+G1D/n+OVW7jfSmO9G0jaWAN42pjNpdbb4IQKGhYmIAklc60az4au24htm6RMeIhylIyOdN8CUd7vsnaCVdwuv1qEBb+2JMIRaUV44mkCrsHvEV+pUxyG37J1pvGklt7NSXLg9jlkrLkTLIunU5Jjd1cG3M3qcXFrDYa8m5ZLrbhJN8KsTVYFs5FcD4ZjJAKwlbRKOPxIX3Z23UBc3qcYF2tmzgV9Tpn3VPJiZiFsLsy+/VEnt42CkfwYT5pfTMF7q5Y0o1yJIr2ey5HtTWcITchJZIHBgoeYwCDFJO9kbEoikIt1YeuuCl0TWBlg2u46ZZSdvZ2Eby0N966Q2j2eGvi5beR0G3N3ShIHNKHauWBLUAqlJ7x8I8R7bkxL5dE+wBPqOO4JfFx7r/1Fh69JsANYw7TyIYJgX1E10kh7c7GrDo2ksyvauLOn4xP7Uy51pXnYibxtqsvz/gnMFL5iHtC0+kn8+jrFJjtc/FvSqPkjnoQsrBLQnTKD/sCDr4+m5Qm9+ALOdFUG1sWM3zucm5LfoDDl+1G7ScIhSyaVq6MKgQRDgdTruhJixbJLFmSxY4duYwYMf8n19GwoY1wuQSbzpwgu1shVSdF4Ur/Cd1HTQfXMAYNWXlB4AJkZRVx7pz3wt8vvbQZXX+CVq3ewOsNIaVk4MBPSU5+nnvu+YI+fWaxc+cZXn11G2PGLObEiZIfHU5Kyf33r6B16zdZvfrYj7b5NaSkROF0aqjqtxuI/1V8473wS46f5wMhRDMhhErYaWD3zzW+KHR/IRXbDEJnbIrnBwkcMzktNlFM5oXzCuEMYwoqsVY6l5tvkEonEhPrcqbVYvb3ewqp2ChSIeFAGp+vexotIZJkmtGAIZyys3k8aSojb23LA/1uYIE+mv4tmrPlVICKrQYiEElIAyyN2hX5zPncon7FA7z43hL6PryDOp9PwJKABN1ygISmJzrjMpxUCbqZ7zzNla3G0KDWzPMXrFOh96VmfgM+mQ4uqbAy8Sy2cCDRyHc/Rfbc2VifPcTcpYu585OXaXm0B2ciw5tJRY47OaP0otAysaTklBlEM75Gt4/hMtZj48SjB3BoNopuERAqQoAXN6u8A0ja1Jt98z8l3VdAUGuB8nBz3G2KQTXxfp3ODXf8jQ7qelQhUIHOCV/Qr+5o1pt3M89wEo8FmAhKUKz3uGzwCHa9kwwB+f/YO+/wqMqt7f+evfeUTCpJgARS6EjvKL1JRxBFmlQLCnbBrlhAUUQRQUVEQFCa9N57772FmgDpPZm2y/P9MQiHVz3Hcz7f9/iH93WlzTyzszOznztr1rrXvVAMsBs+Ejwvo8i0wJOCwblLATtGy6HTsGYaH5WbTt2mH1G6x3vk7+0M+nGqVYsmcvgBflhUA69Pxe9RmB4D+1/twfNt5pOUlIRlwe5ryVwvKEAKyfxLp1i+/AI+n4ndrpKYGM7EiXupVu0rvvrqwF3XUZsm20k98QWpJ76gfesfURyCsWN3UKnSl0yZcvfaX7B///W7frbbVaKj73SxffDBDgzD4sKFbLZvv0ZGRjHLlweuTSlBUQRr117k1Vc3Mn36ER5++LcnRuzcmcw33xzi8OFU+vX79QSMf4bfqg1NmdKFTz9tz4wZ3f+aVpK/pBf+yMc/xwfAHOAYsPdfiQb+Ti/8QdjLKAgVEOBLsUiuspXG5si71qimDSkk4mgR4TKKB5rM5bxrMdubv46zOJomGe9T8sa9pHbeQrXSCcRw591Khv8sil/Db/dToNs5wEDMUIVPO/mZNSMIR2FpvpBTqKie4FCJdizPDOGntFWomVUQCJrsHsroojBOV9vD0KA3kD+GYdcdLG74NVfvfwsNi2JFRZRdxggznxnqOzj8q1Bsb3Mz8ltCvN0okbWOE7HvU9o9Ep0xlO4bxEH3G0i/5HD2QsYnFKCqr9Hn5npqhM/hoprC/KJ0XIpCgQyhOKw9wfpmnOYxTK08RSKa3t4VIHOwlPN8G1WJ01mP8ezUERRYASoMrueBChaKlMiyJag49xOEw2Rl//7cb72JqYzBYVoM9xSishohQsHWHvTVBI5g0q7FIbp3SmDFeKga76WVozyhZzPxjDzGaGegwpFuSN7uW57E5bsILaXyk8NP0PO7eX7YfprmhHIoIZf2+Z0ZNP4bLodsZ0zLp5k+pz5m9yRSv/wGhJ0Uox7th80lOtpJVpaXoRuWMfHzjkyYtAeQxHy7hLCHz1DD6Mdr8cnousWzz66lRo1SbNp0mWvX8hj3dhJxJQoBE8xz3LhRwJgxO/D7TV56aT1Dh9b9lYtXbGwoKSkBVYKiwObNAxg9eisbN17mo4/a0qlTRZYtO4+mqdSrF0N0tItq1aI5fz4by5K0apVI/fqxmKaFZUmSk/OxLPmr7reYmBAsS+JwqJQtG/qH98bPP59hwIAlxMSEsHfv45QpE3is06n99Yt3f0LYKaU8RUDB8IfwN+n+QQTdY6P0CAXLLXFWVokpboywabcLaCZeVN2OcAqoE4x/zFnsjWpwwD4eS/HhD80ld0sejv0KxSFtOf6ISqfKJiWEiocckoz36HpkCEfL76Dexbe5dL+C0wbNonSOvfQq+RFJeMR41JODefZ6EWdHdOcCgsah8wnKL4tmSZod70WjC+156rnW3Bx1jaiiGDTThke1yDfhWEgEaXaFmuxitXsxc0/vR5dtaH2mGzZL4+NFKjXrvkGipznZzsXUIgqJIMTuoXlpL6/a7mekvRNnS+VTx5ZPfenhpukg0/CBCMFuJhHjeRmBnxB9A2bwAqYUvUmwdDMjKg5DkdS9mEROQRGxIaGApGWSypHyJiFISty7ASXUh1Cg9mfXGGHrjEpz4rnJk7S91RFsIYNeQOqbEPgQSBQbRLy8i8T3NxGqJ/Bjh154vTrxK97EtWksY8MLMA1wNr9Gw8+bMfv9DYFJSgrYgwy+LJvLvBXViB7ZA3fV5ZRdolP+2CSsHBdRsQ4KkRSbBtKUeLOhUmwQR48OZ9q0QwwZugy/30SNKSS052nQLDYwFxk6CnIC0eiLL64jKSkbr9ckPa0iGxa2BlnMlgPPM+OHTdhsCpomCA11YLervPPOFpYtO89777Xi4Yers2fP49Ss+TX5+T4cDo1Ll/KZNGk/brdOnz6LuHr1RR57rB716sUSGRmYgHzo0DDq1v2Gc+ey2b49mTfeaIHNpuLzmRQX+9m+/Wogb/wPqFIlii1bBnPo0M1/KzIdO3Y7fr9JRkYxS5ee5ZlnGuP1GgwfvoorV/KYOrXbX7Pz7c+TjP1b+Jt0fwvLsqD/BShjh121ISYQeTjiVKQlOWBOIN95jXizRWD6gAQTC487i1CtNOLVK9iPmnCkiPhGrUkSy5AGhJ6vQZEi+bS9D11cZb6+l+7Sg9dIRrNfplFsHL3Xf0WJ5Lo0umiQ2SCXuokbOBqzE0vVGeH+jEfmzqIo7gzna8Rzz9oXyay9jm9L92DckjCkZZAfkk6WSEWzbGSG3yDYE45b2mlj12ho60pjdqBg4LucwvC1M9hbXqJZKhKJT5MYqkKu60Ei/BPZbn+fi3plaqknURWL3Up7ckVlcjU4LxfwjHye1/17aWv4OK1o3O+dzi/zIGwyhfr5rdgpfXREkKq7STvSihXPlqBKwUa+7tYNywFLG3hBqOSJIGYObsvbHEagMKh6G45IN15c3FDiKMSGR4nnevAwphoTSbF5qSDhXZrhsNXmQONvcWBRZOYjyrfAOh1J8kU3lR9/AfnzGFSHScyHG3iqWA04s1mwaXc5Wsdco9UZhSmTa5Gd60SciKVoQ2XCHjyDElPIJ+pCotwxzMjeyLd9L6O4vXTp0oAmTb4nM7MYny8gkzMzg9FTwtFiitCvhyOKXWiaghCBwZSGEYgsg1wuKLGRggIfXbtPwOs1cDhUJk7sSI8e93D2bCbjx+/G77fo128RXu87xMWF0bVrZebOPYWum7z44jq8Xh27XSEyMoiYmAnousX777eiZs3StGlTjtBQByD4ZT6q12twzz3RnD6dgZT8rjH6fffF/dsOZQ8/XJ2kpBwURdCyZSIAc+YcZ8GC03g8Bk88sYJdux77z/bi/yIkoCt/lAL/PNuYv0n3t/BuMngsuO4LDJgc8Q8icgMu2pZhk8FI00KnmFz9CpNsj1OtdBD9Fy9E/JCBcFvIIedpefwj4vY+hMsXS8zwOFIW5vPBMjt2WZ63nh1A3r7BNDs3nOOtBBmNNxKUE0dEch3qp2iYKSXIrFka0U9FsVQaFVTBboLdF0S9nyYQnBNPiSv1iW8tmdg5i8Fnr+HLjuWNxTP56OGhOPxB6KIWSWHTKVkoePbjEvirLGfvPcvYa7bgVDeD+ldVLBGwFt1U04+i6NQS53GLIkYt3ULtAVMQDh9Fy19md+tGt58GnwjmR+MFMuylibM2UdVKoU6hh6tBPhBQMi+W9rtGcd11lVptviA2044z6gJZ+fHcvHKNhtMnUvH77RD+FshahOnreVUbR2O1Nx8Hjeei+hXd3a+yVZanq7Ge5zWd7Sd9hNf9AA9upALHtJ58G/Qpw5QoovKXkinTsFSDGq9e49BjUVimxJYaQ4lcJxmRXux2k1TFRPc72Lm3LC+M6sephz8FE35qtYKtlxIo1EMItjnRk8PJn9KCLrMPI+UhWrcuh36ggLZtKzJqVBM+/3wfhhEovikKRIdbXGs+HFdiIb6rERg+CBh1SHJyPIQE+6hRsyLff9/j9nP4j3nQgQPrEBJi59tvD+H3B46r65IBA5bwzDONmDfvVODyMyR5eV7sdpUePapimhaXLgVmzr311laEgEqVIrlw4TkWL+7Nu+9uo1GjMrRpU44lS3qzZk0S9evHUqVK1J+2XUaPbsUjj1QnMjLotmytTJlQhBA4nRrx8f/dyRe/B0soeGzOf70QgKI/7ff+Tbq/he5RcDFg9ELT/5HbElDTeII92miW2B4gXCaSbNtBgjAowiQj5jQx0ol0gIzREEKhfIMGZDiOUoiFvTgKoYNEocy5ljxw6AkchovSKz5kb8IVopLuw1R0dNVPgSuHiPQG1P3pc3bVzObDetVo8PJe+myohCs3HZlTBsW0M2w7LGhciqiksqgI4nMqMGH2Gj7reIyN1bogRQg2SxCbZ0cc6E3ZIz2o8WEmJfNM9lY0qZipEOrVudn4GBWKX+WmeYLqNhedZ9+PYoH02Ala2YoNtQbR1TmXk+HxKFYRIZ5B7JeF9LTHsD4vnCnfnGRyx1GsqL+PD+evIj47hult3wYpSA1JR4amUXp6HllvdOSR2qlU6DaM7VY+mdKDx9aaK+oukpSyHJA6rxvVWTq1LImPvMpupw6mhlY1DS8SOw58+Ag11uLT6/Gd/XGGX6nLhnLrAq3SPX0oh6qjnc9h9kcerhVF8GVEGmUtOPrZ/aSXeoqBgzty8LAPxk0C/NhsJgu/W0RopEHjjk/ceb2rh8L4xqw/lg0bJBs3XqZmzak89NA9rF6dhN+vo+sQFl6Axx+CJ6kkhvk/R3YLioodJMZsZcuWJtx3XxwTJ+69TbpCgK4HIuaZM4/d9ciffz7DokVn7hxJBHKlAKNGNWXatMN3rZcSLl7MwbIk1aqVZOHCR8jOdlOhwpfcvFnI+++3oVGjsv/Zvvgn+J/uZV27VmHevIdJScln6NB6f/rv+zMgERj/BQr8m3R/Cx8kQK8oiLZBWcftm3XcCE2lhtmfA8ZHFGk3KWnVJtK4h2z7SRCwrMVgEpc0ovSZqtR+9A00BLqjiFX2gEl1+14zYFJNFKnSe98zSCHRbT78oRnkJ5ziyGPPUy5/PJMLPyA+IojuJ9pwz6pRtE6RBFXthi8miwWPduLpD1/AsPvQ/EFoFvQ+bMNQQTElq2obnI+tSlFwIU0uuzhQzsL4x4KBBeUKalMjeSSnY1rR/+m6qLok1r2UIPMMAjinewjttwS5pTqoJmrXjcQpabzLx7xaXES2rRt2mYuFgW7dpLf6FbG98nhy+0SmNi9CyDBM4WfJfV8hRUArZvv8Qa7Oj+O+Z3bTfJCbF4Jb4kYLZMWFCkoiCIHTuMB4ymF2tZPc43Ei+h/AzHMSMfAoUUoY+Y70WxYYJoqVhWpcJX5/GjGlNESQwY1z7dF2ZzI0qAzOuXXpMvgnunpDWLnWzsBJjdH1szRp3oT27edwb2RvJg++SmL7nTRLuM7xU4EmAuH0U2bmz2R0/w49KB5axcL+DFiZTEZGMUJfy6k9N2jRuQY5uUG8/txOnn7lgd8gXNBUk2b3JlOnRiopKfn0778Y07wT5VqWxO3WuXmzkJCQu4topmnxS0CsKII1a/rjcGjExoZQtWo0ZcuGcvx4Glev5pGb68U0Jf3716J//8V061aFAQNqs337tdv3TZ68n7feavG7l76umzz33FrOnMlk8uTO1KkT84e2jGFYZGe772rQqFs3hpYtE/96TRG3IBHof5PuXwRCQJ27u3susorN8nkUv0b73s8wePs3uMeF4BrOp4A4AAAgAElEQVRaG1W3cUFZynzbZHRs0Okg1zoeJMcsJMFqx0ltBqbwglTYXOYpEts/SuWNIyjhjyS93s9UoS9r7h8CpoLmcTHRepUr4Ze4ZKq8sHYJiqXhMgpwmCbgJVbuJqjgAwJyCtAs0AKDhtlTyWBUXx9hbpNdExoiLRtnyuVwbMjTXLxnOKWuNWB623dBmJxJ/BS7OZnI4nEISuDkBwJ2NIIqsipLHyzFgCY90TQDJdiNH5ijmlxxzUKg8oB7HMdFLumOIVwKb4sso5IR6sZSTJ4c4mfkeqhQHMmlkAKEKTk3uRpmnoMdo7pxsf8OPNIMPNcYIO3YzPMM8h/ly6LRAPROnMLpeSuxR6bi31We63Ve45qqU2bNdwTXzcSOiw6Zh1hcN4J3PV0RL3fmpa3TWHhoAf6rrZiak8HUPcfovacf688VkJ8PDodGiQiNi0tnoPndbLiSwLCtLXj2nmfxnrvEsy/lABJhqPivh6Pas9FluUDRJe/WcBQF0rtWZG15k7P7vsJrWYQFGXx5pBwnfqx7+5oJ5Fw15k5dTWJcDrtOTuTKNf9dhAvg91tUr/41Xq+OlJLGjcvQtGkClSuX4IMPdtzW5CqKYMKEPTzxRANaty4HBHKzBw8GfBlOnUrHZlNo2HA6RUV+Vqw4T6NGZWjaNB6nU0PXTQYOrM2OHVeZOvUQLVok8vTTDRFCcOJEOm3a/IDHo2NZEp/PpE+fRZw9+wxC/HOP38JCH7VrTyUlJZ8HH7yHRYt6M3HiXt54YzM2m8q+fY//Vzri/gj+jnT/gpBSgiE545uNFaJTem8lym6ugeZ2Ej4vCB4LwtIMCvTuRC5uR5BPcrjnFBrY56FsqkRyhcPEF/Uks9FxQGITQVSObofPlYOjOJr4A4PxadAkYwY3Kq6hzKm2zBwasPazFJMtNRbS9egQMmqvxRceGCce6tEDSdhbXRCne8ziev1pRFxvSeHBD/BpUCErlyUNVnA8thE2qxZ1bTdZP2g4K4qzb/1hBKJs1UunnHFkFXxH3327qZcczpaaC3lm/4fkheZTNEgQGezGh8okrQynrF04zPN4tdrkL3iMTQ98Tm27detcJHGhi6meZlBQqjnBD37EQm8Ox32SxEI71U3wOw2MMB9B6l5Ke17Gr1Qk3P8DRVoHMl3j6eSegAsvFtDVM4kLMSkA5M6pg99nASquH3vQs5FOUxJxb5nHco+Jx2sjqt8xlpTLR1Q4RJN6V6g0qSmzF9Zh0cECTFNSumQRDWvrfFt9NTF6Ns3626g851kuXMjmkb7XEAJcrhBAJya6mFXNLxOR3Zu+6cM58G5D2HlL82sJtr2msveh17keUpJV6VPxhxvIT9fyeL22rP7UR/36ZVi4sNct+dcb+HwG2vmzVKwocbk03O67CzMFBXfGOF2/Xkh+vpdRozYiBHTuXImjR1PJyChm06Yr7NqVTEJCGGPG7CAxMZwvvuhEUZGfrl3nkZycf+faNaBgnY9KT0cye/aDCCGoUaMk5ct/gWnC/PmBQtfLLzfh5ZfXk5MT8HJWbr0rSkrKoXHj7/j44/tp1+7325uPHk0jJSUf05QsXnyWU6cymD37OD6fGTB/33zlL0m6f0e6fyVYEgZfgDW5MKUCfHKDB048x6nh93DkzWVIxcL6sQKiS0kkJobi49pCD51P21EtCNeGc/+Dw7hxbx6lfk7Ad9Wiw9pOWAPOUVTxAhtrDkVLDKXlhJVouhMpBTGVKlMqNxR7/c95DMkHSjvSXKP4qm0yXY5KgrMSUUwbuvBy0XGTo4935bVZK1AVjWtNPwPFIrXyBnJ8KtFFL5EV1ZNZra5jKgopwVtIsp6hh/4FmsxBFwKBwG7YCFEUrsWORHXX597LIQT7BQ8dHIDDfI+IogJGXn8LGhhstd/LObUKDuMEs79N5Eg5O3OqrKYFKiFFP2DgAiWUmt5JHA0rpnS2whHNpJuAZoAM9XNk47ds2lWOiI4+LMvkI30FugApBZ0ox7tZTbmoxJAN+IGlnMRHZZxcokbfLA6vDQilKw3XWFw0g9k7ytF5a2UmjlnDVxMHEhUbS5aiITUflapm8vUnq3EEWUy73JWZj3xD/54nsQyBY6qG8Eqiguw4HZLU1ECRREoIDrZjWZIRQw5QKzEXFcnrxzbQa0XJu/zryfOjn3Uz/XozxMFDVH5tB3k+gfdyCFlZeWzceIlHH11Cx44Vad++Au3azebGjUKEgGnTHmDz5sv89NOp37z88vO97NhxDY/HwGZTuHIll7S0Ox1oPp/J8OGrOXEiHadTo2LFSMqWDSUr686adhXL0692LUqlhbL4g7M8Nmk5liUZMKA25q0BuFLC+fNZAOzbl3L7sU2bxnPw4E18PpNDh1J54IF5HDz45O8SZ/36dwrNmia4eDGHUaOaMXToMsLCHPToUfWP7rz/U/y3crp/d6T9Fk65A6qFHAO+vAlJHoQU1JjWDneZPBadegfrgQhEkIbExH5ZoeHcXKQAQ4XKLhu1XZL60aG82cKDRHK93nJOlP6KfYzDsBXhjUjlWpO5oApctTTC2jgI71QRV7XDDFZ6keH8Dp9Wm8tRXdlY1U/UxXtxHX6EjZ4c1nty2BW7n9nNPsav+mj3wTaizjfF4Q7hwcUjyQp1EqxnIRU/IFBkDgmHutH7vYMMX/sZNtOGFIIERzCPh4eTYHm5WjKwE912H+nhl3HbnOiKxo6Kjfkq6DHOq1WxhB2fVp+qGWUYtMdGWK1kCDEQikWUfzJR3g855fCQXGUUB+LeZO6i2vzS/CmBhPBIHm1r0LvkaXqaFt1NBakr2AhhZvHHVJTXaW8e4qqA1g64JsBOGi+I3szv9iB7U55Hud6PCxW+BYdOUNOrzDlZhqH9LrDuuSZ8r35AiaLSgOSGANNucN+zJRm6oTGDHjmO3WbhcJrQQkcGQ1EDG17v3SO4MzKK8XgMrNwwhAGGT+HosTK3TG0sNC0Q1QcnQstS5/G9doTN3U8x7XwkeywTme1GSolhWKxadYHnnltLw4bfkZwciLYNQ/LSS+vZvTv5dy8/p1O7rUjQdYtz57Lvul9KOH48HSnB4zF49dWNzJp1/FbLrUDTFJ5q35D7q1ZECDh+IZ3iYh1dtzh9OoNfsgXh4Q7eeacVAA0alCUoSMPlsvHtt93uml4hhCA31/u75xsSYmfFir4kJobRvfs9dOlSmUcfrUVh4Rukp48iMTHiX+24/wosFDw4/9DHn4m/I93fQrwDHErgX1K9ELipI9N9XOtyFJCY8aD47Zj4yBOXidITKXcqCW+ZLaSHluGbbnPJZiymcLGgejHPVDzK+U4TMW2eAPtAwBuhQyo5XX4iWzUJcz9OxudNkOYhbCUVQh8vxBQSKQQvDTRorCp8rz3N54UTKK85qWELxe6qhNCDcHhd1F04lgKbJNwdxpCdBh3OzuSnFmOxrFbEOgzeXBuMKjU6Hx/KxI65mFYRNQ0nXfTP6Wt8xCeufCaMaESDbVl83LUkoZ4V5LjCyQqLpIJxAVUr5KKsR9Prhdj1EFQJcTnVuV76OOXVxtzMSSYmIoWwg3GIUC/kBJM1+n4WPniJPsJN8eUO5C77AcsS6K3exFlzNo69E/go+xGWNgJRLg6JhQJUupU5kQJ0JZ5Xgz9gC4JnXQ6k6cBzqALOuCtIn0b5j9fyg9NgQI++ZB15mvSIayAC01KHf9GCr16cT//82RzWatPQPIHPp/L9iXp073WB6MhCurU/x5I11RFC8I+drMYxH8p8G4YCVw5EUCamgIzMMF4YtpMeHS/Q4r4UTMtJuzL9adjhaQTw0Vub+HlxBqYZiGV+yd3m599JHUAgN5uaWszvITvb86vbFIXb5/fLVyEC30sJGzZcYs+exyhVKpiiIj/xsWFoF1TUYIWexj38dPAEUVEuJk7sxODBy/B6DVau7EdcXEDOtW7do2zYcIlatUpToUIJzpx5hl27rjF69DZaty5Hs2a/beDzC7p0qcLVq1Xuus3h+GP0kp/vRVWVXxUR/7ch4b+SXvjbT/d3IM+5wSehalDg6w0fpyst4qa6j/rms0TKqnxrK4eqBDHI2ogjtT5YXgqdGtNLxvIRP5JLKdp71zHuh0ocHPoUpuZF6E6kzQ+KhSDQ0SZQqFLUm/hPn+dGnRVIYfHpgw+y3bDwqBChCJYSSYOTCqfWH+HwS31ANQm73JgG02cghcRb/iAlLtUnp3oqJc6WReiBjV/oyOOxEfX5btp+gr3hrGywhU+7zifLPpoE6eVYbjtC8GAhOGnU5MDppqSF3MsnDWpgCTdPbSigyu6NbH9nLv0871FL6cSVzaEsLTmdTXXexS7tVF7zOOueiKH29okUVcgl7fPmZH/UFkWV1KiRStxnh3k2YwDVjw5BoHJRP8CMlBm8X+lLzpc9zMbaP/FwxZVUdOQhgY802KSAX0nkRvAcdLUiEbpk6wV44/iHZHyVzRkrGP+lSMofnIIW7qOHCS3WVeRp3U7Ig2epbcJ3RRohQSYqkiJczHa/ycs1vJh+Qdf25/l5+iJKVX+FvPygX73+Lw+K5rP4j6BdOlQ38frtRFV9A7dHEBLsZ+eKOVSrkkGp6i9SUOgEBEJIpPz9olNIiJ3mzeMZO7Ytb765hQ0bLtG1a2WqVo3i889/a8xgAELAxo0DadIkjk8+2c348bvRdQtNU243Z2iaYP78XqxencT8+adwODROnx5xuyX3P94HUjJu3C6OHEmlT58anDqVQa9e1alVq/Rvri8s9KEo4letzL+H1asv8PDDC1EUwebNg+4aQfTP8Gf46VZr6JKzDv2x1Md94tj/9+/7BX9Hur+FnfnQ8TQWJmd3ncFTy0PyPVuw0Im17kWXgSjlIWMVh9SJ6NN34ehajHD4CJWCYCuS98Qj+GQoXbM+Jj6yPjeOtuN6o7UIRWIvisAXkgPSwFJUpDA5ETyPs+/NASlQTDujruQzJOlp6lReSOXwT8H1JskLHiJKJqCYNizVJKf8ER59LpUnNofT+VQtTAmZ9a8QZ1TAc8Yg1yXxK07qpDTn/cf7YliZnIoMIVi/yr1JtQkpHkFi/aOs9LUhWuRzzJVJ09Af+bCgmAoFz+C3edjZMI6VbZ8m1G8yWZ1Iu60ZPHR4BC/wJD77QbYnrmHryptYMpLs2CIUTWIVOVC0QNTasEY65U9bvBu2mknFD+NUbYxadZbkgRojlXxe7/8gfpuXTaag3aKaXO11Cl1AKOC30tH0bPScMuQ9vJExCYtYFLMD416FBj8P4arXhlVsR0b42PldLRZ92oa0/HDWRM2kcbVMnE5fYO6ggCDppXlhd3TvEiwLWjW5hqpYtLg3mfXbKuD3a6AIcGmwogMJVxUYch0yA3KnQ8cT8HgDhFpUbOfTaUPxuH0UFgXxSxFRShFQOdyKYxISwqhQIZKdO69hmpKiIj+bNl2hZ89U5szpSVRUEKqqsHTpWb74Yv9tX95fIth/RIkSQbhcdt5/vw3vvtsay7L45ptDvPnmZoqKdCpWjKRbtyo8/fRqPB7jlgriO+rXj2X+/F6/km0ZhsW2bVdxu3WOHEmlV6/q1Kz565zt+vWX+OijnRQX6yxZchaAiRP3kZX1Knb73T20a9cm0bPnAoSAjz++n4ED69xuS/49TJ9+9PY/joULT/9h0v0z8LdO9y+AoiLo9xj03ZHFox6LkyNXsb/GQqRmIW+VUbLUU2SLs3Qz5lBK1qa9ezK2l0+Avw2yy25EzBsMVJ7ESFbx7XZQfNRHmlqMLz454LsrdcodjkbTbqDb4VqpWLaWa8YB2ZlPTqwCCam1NlKclk2jTQJ1bysYMQyZ/wTS3xNNBnPvtOkk3/sztsJIhjQbSsOcCQizFlL1kXIjmfv7OJm9Op0R3S02T3AxcsU0fFohnUdNIz3kKVqeczNhbhxIhTZno+g+9CekCKUzs2hszGdpqUHEuxdjlxoPatdZ5nubJw8Kuu8vJlmphVN3YSomZW40IGsKmJrEPNOSjOhgSvrG4XhBcl9SEhWCvXz81kbW3Yzg5CuNaXZuGkJA+L4c8muPpl+6B1UJbDi/1PC07sg8/TwaJpluJ6svhfF8311QFBg3tXrffSxsnY/HUkhJL4U0VXJeeogn357DBzcvIvtfotHcIXTu8RgOp0GPTmd59rFDNKp3g32H4th2PJvuna6yYl0C0+Y0pE+PU3h9Gn6/Rv+HTvDeK9uo2244xriT/Fhg8sLQBuhqH4RvPsvWlL/VzBAg3rkLFOAXQhF3ZudpAvQAYyYnF6BpKnXqlObIkTQgQHZPPbWKZ55Zzb59TxAXF8aRI6k0axbPiRPp5Of7fpU+6NSpIh9+uAOXy8agQXWoWbMUsbGhpKUV385Jp6UVcfx4Oq++2oTXX9+MlHDjRiG5uV5ee20jR4+mMWhQHYYNawDA4MFLWbbsHG63gRAwbtwuxo1rx4sv3neXEY7LZbvlVBYYBwSBlmLDsNB1kylTDlCyZDBDh9a9i0BfeWUjH3+8m8uXnyco6Pd1uk8+WZ+1a5NQFEGfPv+3TmR/qxf+ApgzHzZth/TiUvR2XaW4dB6WzeCOM4YJAorEDcQtpwybPwgQ6G+OonjWE0TkxuP6XsNsFEbuqUKEVJGKQpLTSZipoOpONE8859qdw1QFFkUsFS8weFsotTbeB0jCU2oRd/xBEBJh82DpQVwvqMaktvlkhjuokVmT3j/XJanjFzilh3n9VlBlbSF5wfm0bFyDs46jjOyxF9V6iNIFCpoVhM1UCPPEkhYaRM8TdjQrkNhoeE2jUJRHF3bmyjeYG/E6ZHi5Er2FrbltaG4Z1MvT6FrDQFQxiPj+Aw5HxZMZEs6S5heomnKd1Ec9FEWXp0BUp8A5EEJMynw+jQ8Kv8XwV2NnWRv6jRLgs6EEScIu1SGvjovWpd9jj/4Kefpp8oN60UWdg8uvYwH5mT15qv0tL+goG+T68Gs2vqjWi+CupbBO3EDkGbhCI3nqjEaQGpAnFRsOLKlgGA4qVh/GiXN5BAX52LK7HItW/szXkxpQpsw6vp7ZiLLd3kNJ9wAW85bW5oux66hVLZ0T21w8M60ry5ef49KlEUz8LJ4bqQ7uhLG/kUL4JTLV7w5RL1/ORYlz/Wq5YUi6d59PYmI4Bw/eQFUV/P47Rb3atUtx9mwWpmmRlJTLpUs5SAk//ngSRRGsW9efzz7bc7sVuaDAR6tWs1AUgaoqlC9fgpSUfHw+kylTDgKwe3cKPp9B27blWbDg9O2cs5Tg95u89dZmIiKcPPbYnQ6yli0TmTGjO999d4Rt265gmlC1ahQul40hQ5Yxb94pNE1B0xQef7weq1adx++30HWL3FwPaWlFlC//+yPlu3SpTGbmK/9WSuLPwt+R7l8AlSsG3mGeDg3ls8VLia63HVU4iLdaUd7qTIFIJlXZj9MqwVptKJ2MGSihKr6pJVnQpRc+VyHlljegw4jXUc82wNXcpHirQlboTRaW2YReUMzDrlJYnbYGLK4EYClUyHXT60QoimFHSEH5PY+ilBC4IwSjBngZljKclyr15koVDamY2E2Ty6VyqN14Nhu9qRx1hXF9YEAg38E4wUPGfsL05SQHd2ZyO8GQ3Sabav3EzXAn1fTz9C+xALf2PtK0kxWZj2JCpMghR40MkEdJG5qVR1JxHBvGdufJEdMRoQVIC0S5JB7ulUahI4iq3vo0GprJFrkDzUrDUMogsYGicLzKUM58+RQ1b4Twls1k5cwtpI9Ox2wdywPRp1hmFVJFOcl+exfSbU9hIfnY5aKlvh9F+qlexU7zh6uya2J9MCUM2YYsF8KJD5sgghWCVi3DuWQ5NYbvJS5bh8saUgjGjGnH46OOEBJiZ2i/SyRG7kFVfFSvks2o4Xtp9E5PnA2iECl9keFOrBqLcabmUat6Gjk5oRw/HYNXN1iw4DRbt17BNC3q1HAzcvh2Nu8sT4NamYz5vCmW/OPCH+u6+zdvd7lsFBT4MAyJYQQIV1EE0dEubtwoRNcDhHrxYs7dx7Mkixef4w7TB4jT672j/c3IKGLMmDa8/vrd1q5jx+5g//4btwk3NNSGz2fh95u31BA6mZnFREW5bke8ffrUxOWysXdvwNe3RYuAqU1urgfDsFAUQV6el0GD6pCR8Qpjxuxg2rTDPPJIdcqV+9fKhYA5z/89JBYefl+V8b+Fv0n3H3B/G1i3BK7fhIcbfUmx7TLBMhab6cIjs7AThmq+RJ64xGb1eXTcOEQo2f2y8QsPpqpztcdhWBHoZivZOZI97fsyxbOMVPUBspxvcp4plBYbQAo0TyhVNjzDyj2VcVZV8MrA2B8pJVaWwvWYY+TwNiNqhlKgaUiVgDZfgdX17NwjbFzUvRQ6WiFxgFDIt9x8KRoxekkpqqe4mdx+PI+8PAshFRK8K+kjthNRcxa24gg8hfG8087L2byJxFlpTHEO4eXQ90GxIcxw7vtuC3UjnKw0gnhKjsOjaHTuP488e310VE5pbSkUfXjaN4Urpz+jxYKWPDemBdlKLCYOvm6j8dl8OF7uCLHNLpBxqBdShLBvTQHfrOzMvvsyeSjsU1xKLm6RwnX/MV60l+MH33Gkbya+Ng0Q0U5kkIY6qxmt4lexQ22KKS2Cal0kquo2UiTsClZo+pKCLnozsFQnej3ZAZtNRTPXY+UFiMPpMHELSfnxS0hCUMoII115hY4He9Nt/g0+GrucWq2Go5sCm01h794UzOgchGayceF0IsI9vDDsKH77eM6llGTBwgsAREe7OHx4GM89t4bVq5MwTUlYmJ3iYv1XnWe/YODAWpQsGcKzzzbC4zF48smVHDx4A123CA628eKL9zFz5pHfVDH8gmnTDv9up5gQ8NRTDRkwoDbvvLP1toEOBCRoUVFBt9IGktKlQ7h8ORdVFXTsWJHly8/z4ovrady4LDt3Dr1NvA88UJXly/uSnl5E796B2T9ff90Vu30dJUsG305bhIc7mTChAxMmdPg3dt5/BxKJ/ie6h/1R/K1e+BfwW8Xk6Tc4qI2jkzENgcpZ5lGJ7uzW3qVAJNPEGs02bRQ58hx1zg2injGagorn2egaho4b0wphuPgBQ7gIkflM9Iwj8opKlWVv4CwojQKoUtwOXCzFQFd1hj3ZitTI84CLfsG1CFdySMgtS5UsnYkl3mN1yVBivO+Qb1ylMHgxfhysyR9A/I1wPPMW4fIL8oJy6T2yHA7pYpKykCQtjEeKuxEi3Rw4ncB31UcwWXmXUFlMEUF0UyZzMKwkzS4v58vZY5jVzMbEDn4UtQgfdqQIvAWMK36EIPMgulKbVekDqPR4Arbd0by7eS9jWw4EIRCWJD4/G7tyLwA+tTY3j09mfWYfmjVIwRKC9qXm4tE8PK68zX1zc6jbuhhVC0Ruo08MZGzzsSgOSQnf11TUp1HLNYByRgIF/tOEG1tJNVOpsKIlT7XbAQiCIh5FiZhx+/XL8q1ho3c+9TK3s+aywdT6N0EBdUMVfn5gETWCayItWL/+Il+MH8uoETtZuKIGxQ3v42Cf9wAYa1r0sVmYloOaLUeQfCOKwYPrEh3tok+fGjz66BKklOTl+UhNLaRJkzgeeaQGy1adY9vWa5SOD+XmpUCnmBAQGmonPNzJxo0DqVo1Giklb765mdWrk7hwIWA8bprydmHtj6BcuXAyMopxuw1CQ+2cPDmcxMQINmy4SOfOc+86lqYJfvjhQe65pyQjR25g585rOBwa06c/cOtvCUynOHx4GBMm7OHq1VyCgmx06lSJ5567966cr99vMnDgEo4eTePjj+/noYeqsWtXMrNnH6dfv5q/8uz9s/BnqBcqNgyS4w5V+kNr+4hT/331ghDie6A6sFpKOfY/XfNXhdvIJtU6yDbbSPz2QjobM1DQsDCoSFcuK6u5qKzExMsu5W16sx4TH+krDS45T7Cr2iNIaYCAeKUWDQjnFAYQQaPlX2E/ZaFYEpslsIRJQewFIvKrYRZLLGnywxPTqB5nUexxEGGqxMhMEvR82psXUSMk73mHMUuuB1kKIULYl9GTilxGINCdMVyW4NMkyVECj1qPMsXV6BZeB8Xm5ZmgE0RZOUzTv2bQ/K4U9/kcp/CxVDUoLZ9myk/fsS4kl0sxx7Dp9TAVHb9wAEpgJpyZTZB5AIGJyzxCXlgWTTd+S/i+0szr15SkvdksiI9CCkgNM0gsUlBwU8J3lmqZ0yjX9CpOoMhnp7SVzyrRjjB3Kc6XsXhGc2O3Sb73Key6twtISUJhB54zLhAvNR50f4uChuLsCkY2Ap38VjvZvieRqT80osvD6extdZXsM9lMrleBOWWb8W5wbTZZfVn/Vik85mGEzaT5rgQqPhBJ40bfcfhwKu3aJbLih7kEOQ2a35vCZ5FRHDYCr9/YXQnYM4M5ldScc0nhgMGPP57grVFZ2IqfoWHNSnz/U4Pb186OHcns3p1yO9L9hXCjooLIyfFQUOCnoMDPpEn7+frrrgghGDfufqpVK8mQIctuF9KcTo1KlSIZMKAmtWqVpmvXeb97vc6d+xC9ev2M211EUZGfFi1msmBBLx54YP6vyNswJMOHr2HSpE5IadG9e1U6daqErpu39MqS0FA7c+Yc56efTt7OG2/YcAmbTaVFiwROn86ke/eq9OmziFWrAlF/376LyMt7jQ4d5uDxGMyZc4LU1JFERPy5zQV/FgI63T8v0hVClAbWSSn/qa3af0S6QoiHAFVK2UQIMUMIUVlKmfTvrvmrwi0zmae2xlC93JrwSKo4QBmaIKSGTQ/DZS+NQKDiIESWAQNU6cDI8pPd9NasKxH4FEdzlh8PY8XFYqonK0TclJyNtSiXa2AoJt7wNC72n8T9yTPJWehDlTb6Lu3EzhdmUiLkHqr+9By+Xp+hW0EIKTCFJMeucCynGfttTRgd1I8du0ZTUvsJf2YNkrqmURxtkZjecg0AACAASURBVJihUCEjDM2aw46SEViKoJbvGhdt5fALO9XtVxBpUbi/OMaVmMOMHdoZJFRoMYZ5rhtgbqRNQRybvE25rIQgsGF3dKMTMzioxuMxkqljWXwSOpojtppozS2++m4tU6fNRH/lJ3zOTDTjKvts3Qg29jN2ZQ7vdJzLKzZ40w9HjFqsFO2IsIroVpDES3UkuUpgkP0jrt6cCGmGkF4muDN4yAKkgRSgCB1v8XHsGhS77ezYn0ivx/rg92tsfro57nIqxEWzY9QmmrnTEXOz+bRlOVbNnsfHXzdj/8VoWvV8gGYtVnHiRKCza9Omq7g9TqbOqsHXs+6l88C6hL60gvziIi6ObUf/YxVo3LgsEOgki4pIY9STk1FVyZRxF1i7uTI30+74xv5WaiE728M/ZgR+Ma0BWLDgFFOnHrpLKhYoomWxZs1FXn21OS+9dC8TJ+4nLMyO32/eVi6oqmDZsvN4PMZtlUFOjoeZM4/dLs4pimDQoNrMnn0Cy5J4PDpPPbUKv9/E4VCZO/dhvv/+CDZboKB3771l78rrQuC4Z85k8sorAU+I++6L4+bNwtv3h4baOXo0/R+aOORvzk77q+B/Ib0wgTuSlt/FfxrptgZ+mW63AWgO/E9C/ZdrhBDDgGEACQkJ/+Gp/PnI4QIWBpbwB9qiJFxlM/Wt58meruNP8eGs3Jh2j35FgXGD6o5HAg+0QXg7OzEn2nFZ/w6fmkvNpOcpu38Q7tM+Oph3nu4qaQrjH8ogMWgH4RVnELd/DEXZBgHKUQjOKocztwyuEBdNznTn3KzW3KhwnvnBaSSWH4XlTKCCdYrnwr7AJxwMfxCajX4bm4S9ydvomqWwrZrJ/goG7xXc4E3CyQgS1DtYja/y1xDnLmJPnZ/58VEvda6pLG2YGvgTTAcj3GEoYZeRqo+gyCRmuM8xxAZeofCQfQ4lFTtlg8ugX6vC83IrXziS2CwD7aTVfOex+T2EXzhLt0aP00rJ4/iBb2hTIRm9I6wqKMkWxU9fv0bwS7V47Yl3eLL2BtQgi83OkTj9nwBw0d0S7Zk1RH69mop5HgiFC5ei6Df8YUJDfIx6uTEFHXL48vx3XJrRAsOw8WDn06Q1rc4+VYAlcGsG6+dkIaVg2+7ynDpfkhYjfUwJimNX5Wvk3xCgCljeASqHU/Z+Bd91CxB8NTaZCaWWU7taWV71b+SYP40dO+607v74zWIsCdIQmKaC23O3LKp69ehbwyLvLoL98tb900/vv50bPXYsjX79Ft9FuL+083o8Bjt2JNOixUyyswMFOb/fwuXSbpNuqVLBjB+/5/Zj69ePYcyYNhw7lo7drt7ye+jGoEF1adAgli++2MfgwXX4+OM9+P2BYZqqKnjiifqcO5dNWlohEyd2IiYmhJAQO/Pnn+TMmSwaNy5L69blmDXrGMXFOtu2XeW115qRlxfwAI6JCaFDhzmEhNjo3r0Kjz1WjxIl/iUH/ddg/XuFtGghxD/mP6dJKaf98oMQoi1QTKAZ8p/iPyXdYODGre9zgPr/yZpbJz0NAjnd//Bc/nTEioaUkrXxm0W0Nb/Ap+SRwg7It+O/4QUJ3iST+OK2FJ/Q0ZrbsTDxU0hExxJEdKxKFY5QfNJLzjwdt27cNYtJIlGloPf2srR77QEapnTg/eOReNL8+MPScRSWxh17msqOs/QqstFqjI8zONGVumjSpK0xmaXelbh9EhUTpIWpKGy5xyC99AXaHv6Mkb0bsKWGgl+Fn0nExI0uglnYWHD/Dw+RcEHjehmDdc0s1tW0UK369D32MIP3DMZX+ROMaIFpaeTZSjBbzSIPC7A44i2igyuKi77rpESfQ79ehtHZn1P3xA1KXg1COrYxbpSP5eENmWdm0cDm5MsqNxEy0FXdM7aYs2vqUG5fBB+9t5hSJYs4e6EkWyObU1DlcbCa0d22BnPNEWYsK0nI+M28HqozQwpeHXM/R0/EoqrQcs8KqrfaRF5tk4TFs9h4fg7Ss51S6gt0uzCJ64c0+lpzOdaoJMdOxeIMhsZ1tmOWsBF96UvybwpQTbDbIC4YKrjwdakK0wKqAMsSvDxyE+VO9Oe+nztxpOKs26+fqoJdkzw0pA81q2WyYVsF8vKD0DRBmTJhNGpUhhkzejBp0j5Gj972q+vL7zfp2jXQMrtp02W6d593F+Ha7QrDhzdk0qQ704F3706hZs2S2GwCwzDp0aMmBw/eICEhnE8+uZ9atabeXvvSS/fxzTeH2br1CpqmsH37YBo2LItpWnz11SFSU4uZOfM4miZwOFSmTu2KzRa4QCdP7nzXuY4Y0YgRI+5MDDl5Mp2wMMftQuH48Xuw2xUs645xEMCbb7b4w168/y1IJMYfj3Szfi+nK4SwA+8APYFl/+pA/ynpFnEnjA7ht41z/siavyRUHPQQPyONwE4wTC+n1R8hzIettEBPk9hiFTwXdFAlF5UV3BB7uKpsoH/RHnxHVOzxKqrdBuiggBICVgG3i2XFdkl62WQ0QjkU52TAMA9H3rORU+EgZ3p+8v/YO+vwqK51/3+2jGQmbiQQ3BIIDsHdoQUKtNACpUChQoG6UWoHqQM1SilS3N3d3SVAkEASAnEf3Xuv3x8DKfxOj9xze+459zz3fZ55SDJr9ghrfWet9/1+vy+9HVeJd2lk6WW4oIB+nynvlSTuylGckg+zwP4G3TKuYEluTHI4/Nwzg6/3jqLVzSQKbKPZVXc6QlKxGoXU1O9wyJyApsLFcgZVMw1+rO3mAedUliMYeXE29au9gy3+CLIsWL+zKk8nLCGm4iZkz5+Q0Ek1ovlF/5RzluZg0bhddiD+rzZjaOgUQMUmGhLT+XOUs6u4FFWTfbUa45T80UQ+HuAHw05h9yskdG/NG+bPGZ6/mN1LLeQ66nKwUiA1nh6NOewaogeEhLRktcVLsmLQHoi9oWBTAZOXWtXv8ISh84sBebLB4WrDeN5/M2puN/ZbBtP+6+fYnl+Z8we2cO5yKFXq9CJIb8jtq9EMGjaKLOHE3u0qvFAdRwMbGDriaOb9GfBAnaBySzK4m53/iNKsTZuKDHp5AJHheXz5fQt0wze1NU2Q759Kl3ei+PRPe7iTVozVquDx6MTGhnP5cnYpuI4bt4WNGwfx3ns7cTofXfgej8HPP5/+s3l59WrO/QIbLFp0nt69Y5k163EcDi8RETayshyYTDI9e9bgzTd3UFLixW43ce9eCdOnH2PGjBNcveozz7l1K7/0tYwatZEVKxJRVYW3327BxYuZjBmzhTp1yrBz55BH+LP9+68oBVerVSUy0ve8Lpd+3xJSonnzmL9p5XjpUiahoX5ER//3ZMr/nfgDc7rvAj8KIfL/lvcw/OOgewpfuuAoUA+4+g+O+feMEh3MEqWAhEq+dIP51saYXg6m1uIPqBrWETVEQY1zs1sad9+sxUzWz270TAVJhqixNkL7WSk+7sGdaqDZi3GEp2Bu52CzYcKIexUTi9AkCyVWAxtLiXR8SUqul2NqCN1FPiEeNz+vVsnSVRY19xDof4tp5p1M8xvCcvlpND8TnbIlFv9s5UavNRzoFkGeGol/eBDB7k9xKM0o45rOZM1K3+AFVJDCebZpAPW656BLvgnQCjPn8ND/yRL2pDqorRpIEvTqdNXXQdY6nFjtCKn6Vq7aV+LEHyFZeHuTP6P27UJEXkczzCjCilPuRPXVY5jg+Q5lkBuR4/scJQksyPSQYsmydOVNy1DcksxqtTshWe/xfb8LRJm/whx2rTTv+VwdhRShc1JAm+P+/NBtNeuT4/Bv6KHrE5cwAG9WHLfL92a6toIS7yxectmJTxhGZoE/vaskYT3WlYT+3yHlVATDQbQlhcpljnOCOqApRDX5AnfeVormV6ckqRb2UXEUJOXBwTv4v1kDo3oQroG7HqbEsn9/CkIE49HLY4jC0r9b6twlctscvpEgv0w9Mr56jB49qjNiRAP69InF339yKcBu2nSdKVMOcPas7zRqsSj4+ank57tRVZm6dctw8mQ6ui6QJJ/T1wPeLviAefXqy+zZk0x+vpt27Sry1VddiI0Nx2JR+fbb7rzwwgZq1AijVq1wevd+tKD28M66pMTL2rW+5blx41UMw7cbv3Ahg507b9K7d2zpWLNZRpYlzGaFt95qzpgxTZk69Shr1lzhww/bMnBg7b9pej5x4n4mTz6AJEkcPDiMBg2i/+r4f1b8F3e6fy06AR0kSRoN1Jck6RchxPN/afA/CrprgQOSJJUFugMDJUmaKIT44K+MafYPPtf/bCzOhOeugV2G203AoiCjokgWdMmDUHJRXTaKj2gUH9Cwxio0HvYaF+R5hBjVSao5l1BTI4LvxmM4QG6k4lzuQjYAFM73/ojCmEQC7jMh3hLDWcnrvKK3IWloa/pW64FVWFh/PpTsMzcxtEg6pJsRuqBzqox9eGNq2lsSK9aioKN4VWLyBKllBJXPPs88dQSfdTd4+sQygt2vE8JcvvRCawFZ2Q2QAmahh/SiMjJ3MTCAC8KBW7+MxxJIpyqvkpKzCNUw0GQ/ng2P5A0hc8Sw8Zn/djxSCEIygWHw0rFiyg7tiRKUyuX9P2I91wu5+reQCUpdD5hBlgTiPmJdx2AYZbltfZspZAEghMHbbZLo1fo8ZnW3z12M+9SqNZ8xv39vNFsW6m03hqzyWKUkpHY+6aowIOFcLAfynqS4yeO4XLMI8BckLfiFO2v8qRLsZNSST/hlwCcMH9SVbz6ehyRJnDjj6xFWsr0mqTkL0cbdxrhrptr6VtxsGeFDpIG7cU65TidHEIWGiSMPTZEHRbKUlMJHwCukeTYWk8Br0vBrfQsQ5OU56ds37n5jyUczaKtWXUbTfKA6enQTunatxoABK3E6vcTEBBIUZGHXrmRMJuUR4cPDryM728fl3bPnFhUrBpc6exUUuPB4DC5ezOKbb44+Arg+s3YTLpe31Fv3QTzIE8uyhCxL3LiRS+/eS3nzzea0bl2RDRueYerUIyQklGPQoLoATJ7ckUmTOvxNsP3tfSeWfvl89NFe1q9/+u963B8df1QhTQjR5sHPkiTt/WuAC//gkV8IUYivUHYUaC+EOPf/Ae7vjSn4/6/zbxnT08ErEKoEZhmBoIg7dCn+mQTXOzRY8hVhqU1KOzK7runUzx/LMM4iXQqh4uFnCE6pR0lYCscrf0JXbnA+RqfELNBMGo5Qn6rHQAcBVTNNLJ9cl56TrHykRpPl50eaVeZjcxFXmlfmUmOBGxe6pHMudDN/upZJAQbjpd7MkaKoI5soqKpQIVtGTfHjw/V+hDoklvu15+6QweR+05oK9xs7CCFBxnJm7Q+j9rWWdE/5CqcQ5EgqTqUaUSXjKNZP0s9iY5rJyo7A1/lRKsMy2cKQwKlcUmNBaNi8h/Er3MGaXktRgpNRzMWoXT4lbnI+dT+JpN2857l5swqGIeExJG4AC2R4xgRdpUM0NE4hAS/lH+fQZ+0ZXP0qqqrjNbxgGYFkGwdBO1Ej63F32XqkjGpIXbxcDQtk4rmmqLE+q0RFgmHRB6HjZvzuKoQsGsG7X82juP4yqk5YjWvEFH5Zm8+iH1fy/aR5uNwWGncZSXJKKI0aReMXbMWzLQhjnxMS87muCgw/BUwyVAtE1wXbp56kf6N0Hpja8JCVudmsEBHha7WuKBIftBxDjZIgAkokwqc1oFZkEXPn+rr/DhmyGqfzN4STJIiLC8dmU/H3N1O/fhRdulTFalVxu3VWrbrMkUiF+MVdGDW+Bc2a+b4ooqIelRQ/6PLQtm1FAgPNvPXWduLjf2TlykRcLi8Oh5dffnk0VTF6dBOOHh3B5593pnLlYGTZV7SrUOE39kWjRtFs2zaY8eP3sH79Vbp3X4QQgkqVgpk+vXsp4AK8995OFOVTWrWa84iU+ffC69VL2w+Bj4b2rwqBQNO1v+v2d19TiHZ/a8w/zNMVQuTxGzvhHx7zbxcjouDsDV/hS8AB5QOuKMtQvXa6rNlMdO+yaK118ta78d4zUIIllCAJz10dmx6NJCSEbOCyZ3NJ+pWLoi8DXrTT8rqHQaEfYvJTABsR1MGd5ab2/E/wz4+i2CI4XUEv3eltqKezXipA1Up4rfA7QhzBrEn4iTfX9qBD/WzizSY+IoBrqk5ilOBPZjM2t4QugcMkcAzaC1eqUbKrOs/FD+Ltlj+RVlieEct2cKx7N76Y6xMQbPnITYlFAwRmcZdI90TOnQpib+ozFA8cSRB3KUD4UMIw2Jffnx9MUSwJ+o45dZMZlQuyYWGntQXtj61h7z2N/VoUvboVEmQRKEDm/c8SCYpFGmWL2pNqX0H1na/QoDALUx3PA5IIiSeqEVZ+HQcO7aJ8hYqsnSmYMak/HVons+Snlbz65EGE8HFJJQnKRBQjuQ28cZt40y1hCIVt2yP59K0/0aXNWZrUf5Y+Pa5itWqYTCpTB1+jQogftRt4WZXehW/23+aYoWNSDCInbCF13SC4VgBzrgKC8HAzfuplLJYyuN0mZFmUGr9UrhzMrVv5mM0KUz68w6Dm/Tjfpw3bLsahGxIjhtWhZs1wjh5N+zMK2QMfhRo1Qrh2LY/hw9cTHx9JrVoRZGaWYDSPpOinllywKty5VkzxpEOYzTK1a0eSmXmr9DU8+Hfy5E6cOnWXH388icPh5ebNPGJigkr9FwBUVcbf38SsWacpLvYwd24fnnmmDvPmnSUhoRyDB68pHdeqVQViYgJLUz1/zRv366+PIISPhbF06QX27UuhZ8/q9O0b92djk5PzS9sCAfdpeP+iMASa+/9kwP/0EAKeHwOLlkFUGYgpB3N/9PkuADAqCnqHItlkhEUix0ikl7aUYlMGGdoZygfGoAbKRI1W8WYZmMJktALBve9KqKaMwVUxldxKp7na8gfCkhI4tCScW8EKy5vvYoC0FnPodkwmX6bFZdKYXbkQ/zCN8BgVl4lSLxXjfkrZa7JzpUxL4u8e47vZu/m6q8xps8YVNIKQ8CBwyNBjrIOXLliQaig47IDdBAoIPKQHTuPHojd4Y1s/cl1LaHPZjVmzIiExY+Mh5rZOYvj2I7RJVXg+fhA7Byo+5dmWfRQtbUegXozzpAtrQjDNtLOkKz1YLSDRFMvQ4OksK3yB0a75jK46H9d1hcycEI4GF3JKQORZieYXZd7uK8gJpNStzV/bzo2bgWimHEwqyIqvS1Knp7Iwm5uSU2IjJriAa3fDMYTMjn1VOXS6Ku2bJ5XazRQUmXln0mAUScdR7EN2WTa4eP4uthuZjP6xC80a3SGvuAMW83YSrwZy/WAh3eK/Rb9tJuVMYy4ea8vW3kvJc/vRo/I1qt1oTe4hF6qnhLoNM1g1ZzVBEQPYsj2V22lBPPZ4Al9Pu0XFikHEx0fe7+qgc/BINocPt2PN+Tg8hq+t0OoNyfwAOBzeR+bgw45d16/no0o6HyfswVhygg1LZvDCG8dY5ijCW+jF+PgUOSUa4v6xf9euW4AvB/wATAFatZrDjBk9MAyBxaKgaQZ37xaVih3Ax/vNz/edEpYvT2Tu3D5ERwfw3nu+7sAvvdSYjz/ei64bzJx5irJlA1i//mk2b77GsGH1GDZsHUuWXOTZZ+sya1av0ufu0KEye/fews/PxKuvbiMvz8XixRe4ePElqlYNfeS9V6kSQp06ZThz5i7NmsWwc+ez/8UV/MeFAIy/vjH/p8R/HOgaBvcLD79/f0amz03M64XbqZCSBuPegc0rHxpUxletlYBO3u/xpyzhwo0rOxMSHYiaflyS53Mq6lsq0pEm+Z+QEbcHa1Y0QXdiqfRCRexoWDe1xq84iDiHi+kbjrPl1bbkqbUYef9pJoSU8GN/3yL4/KCEzQ0uk3ioJYBE2Tz4anE3TKIbEhIT1wqeOaYSm19EQOu3OV35MY5UaMDtMJn32zvJwMPP+HFjbQfCvt1E54ZrqdjuLsOXu/DLKcAlBrG7eib1k92YDCcr4//EhYABjBrwDRIQt/c4IjodbhYTkpLK2ZxmlEhW6jfYjlMz8XrQCqYWPMl+pTI71YpMLfra51mL72Vb/XQqxmRTAeiig7uSIGqjzN7vTByeuJzX8oeiZVcmvcYgKvXNwOR3lbt3/HEKlW9+ak6Rw4q92wXKn65AYZEVQ/hoA07ZSv+Wi9muDKeJdp6iYhPlGr7PS6NaYPM7jKZ5sFo0unUOYKxpLvEZ92hWP4Nhux9jRe2X+PST5uTmQ6DZzZj400hCI8xSjIGXdoNvotoNPHtNeEYewXvBQ4dWt1m/eClmsw7KPtZvvQCSgr//ZNxunaSk3EcoUrFVS0hMCkQzHmTsBO++0wrDEBQUOAkIMFNU5Cmdo7/NV8GLdc/wasMTWL2CkmVjaNjwLfpWqcWYsUe5s/Ym4neEFm63/ojvrqYZjBy5EUnyyXwVxZcHlmUYNaohixdfpLjYU7ouXnih0Z9d88MP25KeXsSsWadxOLysXXuZoCAL06cfZfnyS2RklKBpBnPnnmXSpI5ERvqaMYWG+iHLEg6HB1WVS+fC7+kiVFXm2LHnyclxEB5u+7vzwP+UEP8Huv/t2LIDnhgEgQFwZAdU/Z0GpmGhUL4c3LkLHg/4WaHqX5GHB8jlECU6qmHCf18JxVVDyP61kIOTP0IoOtdYQ1Hle6RXOAICuqYsgmsNKbN1MCgCr9lAN8x0G/YB58NUfnnoI7+ChkMIVAPSFJ0Z67IYMsgfA4WW0mrOuAay+Vs75oe6EZgNifh7KmV7D8e6/QB6cFdEdjZy3RDqmw/xMzO4wTIoF4j586a0YxqDcoqwdnwH0Woyq/+0nRUv72NhQzvVvxyJZNLIs85Bl/1ACM50bAVbiojutYZfv15OjJ7OYmtfVJPAIcvM0Mtz2BxIgf4DVg0uuesTai7EjrO0TPTA/NAJdA+DRWUFVQtsNHR3IjfhA+7l5lH986+JfHIFkgHB5b2MWdaUrcvrEtjqJkHTNrO8wETbZmPvv2kFY2knXOEhHCtqQH3vJS7nVSAsIpgZM06g6wpjXgpn9143QZrColuxHMvpwLgaJ6gaWIRumMhzq8iKRvkIB1dMtaimXePovRimvLEbpYWGEHDbZMf9bREIM50sKZgJAPJBvwmFAyFoBYryWxnkYbXVTwta4yjxYLJA88YRLF/5NCHhAVSr9i3Jyfl/dd4KxYzJpCBJBpu2p/Lu9p2YTIrPJPw+bdFkkkvZCw/yuA+D92+vCbxeQUyMP8nJ+QQEWOjWrRoJCeV44YWNmM0Ka9cOoEsXn+fA5s3XMAzBY4/5eMMTJrQpzQGfPHmXxMRsDMPnzevvb6K42MAwBFOnHmHKlE4AHDmShtOpYbebePfdViQl5dCzZw2qVQv98xeIr0gXEWH/3fv+J0MIMP7n/W7+s0D3s2/A7fb1k1y2Gt5/88/HmExw7hDsv3WAK8klBBa1ZuiTdjRcpHOCY0whhtZE0Rg3uRSm1SJlfywVLuWT8HgohTdkJMPAnlUZV0Q6hqKTJu0BFWTMOKveJPvDWAwnoELI4xb0ago9ImWeR2EgfqSiM4Q8vAjqpcsEF0k8s91EdJ9wvqAnDgHoXhZkPY3wSKVgZqmuYKulkrvVDfYcss0WrrY6iWxcxN5Ro8zyn5ho3e5DPEnirqiEaoCfYaCYHGiKh+GbNuHOcsGNfHI7j8He5x4CGwiBJASGLBNQTeXGoaX46RcRArq791DGnkmyVBFVZJIvFSEBHXWYGzaKGMc0auu+Y7+BT5ITBExRQTPgs6AoyiVN4PFzGWRnOwh4Zyeuvsf4QoYSr0wvjz/bZzeg7MVvMQV6kCSdtbtr4XT6pqe1jYLULZIyRen0KdqEQMKZEUlacn4p8Hw51UfdcpXkcGjTLqwWjQmT29P7jc/o+Ng6RGV/RFIhl3IjWNh6EpMODWZG+80UVrmPYBKcuBaNpimoks7L8blgnQHGSKAYPDsA2LLlGQYPXkNIiIVLl7JK51VurouvP95C7+5XOHN2IBcvd8XPr+gvAq6iSKV53pln42nfIpw7V2/ywb4meLwGHo9BSYkvLRERYWP+/D58/vkhCgrcZGQUkZ7+l3us2e0m5szpRY8eiykocDNo0Gq+/LIzZrOC06nxwQd76Ny5Ki+8sJFZs3wA26xZDE89VYuXX25CWJiNzMwSPB79kb5lNWuGcfZsBrouOHPmN+HVtGldGTVqI3Fx4Ywd2/R/3Bf3H47/2+n+9+OpvnD8tM8Tt2O73x8jBHyz9Dwhg4djq6UTKtflGgPYZ7yLkHz81Gxxwed3i8FnQ3YQKlRup4VzaLtE9B03BVluWvy8EG3MGa6EzCf9PqHIRgSVSnqQa5MwPL5Cj18NE6Zwmd74oTsN0j4rwusUVOtpMLuNRtJ3dsy6bydrt0TSVnqZ8SWvcltzsTKwJosSzuJ/MYLgbhbuNZbIBybV9eDKnU7bgLW4NAu6B4r2GNzw5hHITCqbB3BTLo8mmbjl7s4ccw59XHv45ac6OLJd9318BVFVh5FoC0XgOwu2zTzFCXMB1ZnEfLuDMnIEje75Iy/9mfWtnqeq6Sb50QHkmQUufC11zro30yZ4FYm5HfDXcinONJgQKXgm8CN2uT7DlWZj7aRBTBxrp2mt8Ux4o4RvAp2gCDyawk+r4nnnve4UF1tJrjOGV3vup/zAk8wMcyJkMJl0xN1UIrrOICLXTcjqfMw2jTHv1iF66UL8WqSQM7EDeT81Q5KgY9tkzGYdi0Vn1HOXiI6viclkEFGcSpoRgEXSaahUgDI1EekXKJQULpwPIqlWNt/1v0RAaig5kzqijj8HYR4uHP6FDydF0KNnXUaOhhYtKnDq1CjCw794ZKf52hg7I4ecwuanMfQVN/uP/ookSY/kXuPiwvj66668//4uzp7NAO7XJ4XMwBnlMIyyvztni4rcDBy4isJCX/+xv2QZ+eB6D3KyD2hZTqfGAk9c0gAAIABJREFUK69sAXy7zKgoO+XLT+XOnd98E44eTePMmXQSE7OYObMn/fotxzB8z20y+UzKe/WqiSTJFBW5+eKLzqWP7d079hEu7/+m+D/Q/W/G6JHQrSPY7b4iGfhAtqgIAgJ8E3LXXli3J4chT8uosgsHWZxjJshGKY3Sdzz2/b5ghkbDGF8uuMgtCO5gwV7XhOznj2IvhwUL9ziJjEq7mzNI+zWP1KYrCdFqUKtud0zhMgtxMIp8MMNnNSz0PmtiYXOfg9WcVl6GHjZhNQRqiMRCp4mcfIUP9sjkBLjJ7naVmn0qM5/RlLCRk3RlQ8AnlNiq09/5HnHhazlzL53Q1w+DUFjp2EzD4l+5J0dQO2wPn0nvoeV5GXUqA/XzPSBACTJhrOtKctNwZAQ6gCRx50Im0bVH0yEiEF21cg8zN8McVKu4idoVLyOp4Ce5ieI3gVY1z0Ya5Z5klBzMtIV5RGep/OAH1tdkLoY4WbjpPN4PdYb3GQnaacaNltEuxvDdmloAXH+/O6LYCghMThNd9ULSj1Zl2GtXCf92LetXx7N2SxyplyBV9WPp2ob0f/wGFR8zcLa4jezvJezDXdTfGk3/qldoZM7EZAgMTaJscSw2u5mDe1ui5Q7l46/a0LRBGl27v4/oeRgppx4x+gXavdoO+/frcSkQPOo4L7tUXMXzMft/QeMO7fB4dNZu8VCl3FE6Rl3mLo3+7Gh/+Jg/H3/egUlv7+DAsYqAr7vwA8CVZbh4cTSyLBEWZqN//+UEB1uRJImLFzORZVAU+REBxINwuX4zt/k9wFUUiejoANLSfLxhXResW/f7WiRJglq1Itm5M/nP7nO7DebMOYvVqj70/iSys98kIeEXvvzyMCaTQnLyOIKCrOTkODAM8W+RKvhHQhiguf/2uD86/qNAF3x5XF2HH2b5ep5t3AaHj0GPLlC9CmzbDYlX2lJxzmDiW5+jYf0EzomZhIt4IvRGnPOuQFbdqGYdM0FE1bzJOXk1cdZhVLHGAGAKlyk+5SFvl4PCOgLR3ce7zUvKIPG5j8kvfx7JUIk2RxNFY3bj9mU8ZThUw02vsyp+XnCb4JuuHi5H63y1XOFDx+vMCniXpRsr0PnqdTRVYkmZJBY3rU4tNqNIAh3ZR+FSJT55Wmdd1gBeHlLM3rinGHTwNVrFbgcgysiiip5ColQVKlkwl7PT4iMXJ56rimYTeANtODSd6tvvkds8gmbB/tRLD2R5bchyGVS0gSpDtlGRyPIyZe9T2TAA+bf21R7JTCb3uMk9KqebkJBwCcHNktpUCZZ49tl6YOgY15KRgsAiGYyMTmHVtk4Uv74X2WMme3pz5NsBfNH7MJ37t+XJBY3ou2YqvbtfZcu2By55EpIqePmdnowdr9JzcDRCW4hRDOJWVVY+tZ5Qz/2d2w8SSCo27yHIG0u9fp9Djpn1C9Zy0dSAQDmHzljYqtZA0q+zecJOnpN87Im2Grz7ygFsNg0Kh+D1vlM6t95+cQE/d9nOlycTMJlq4r3fmsduN3H4SAbnzrWiY2AuvWulsvZShUeKSQbwyZyTDOtUnYSEcqSkvAZAamoBb7+9gwoVgujevTpJSTm89NLG383Xgg80FUVC03xm6YGBViZMaMPWrddJS/OlWCpWDOL69TzApyB72MRc133shr9k/mUYgl9/PYufn4rT6fPmtdvNXLuWi2EI/PwE6elFnD59lx49FgOCFSueKs0J/2+KfxV74X+NH8J/JWb8Am99AB9O8gGuYcCmbTD1R0i8AiCz6ZMJ1L6xksssRpc85Es3qSja0tH5M1azhUjq87i0kH2mNzivzGa79bnS6+sug5zlLowsGf/99bFlxmDgIbvJPjy2PISqIckSLiMPoQtex58QcgiWMoltNAjHs0cYazIhAV4FMgNBlzXOGJ0ptho41SoISQUs7JVlfsLMYaMPb4tNzBcfAmDyQnSRmzXdjnEgzo0mB7Oy3hQ47fsvPanW57pcBdnko3Isn2FnZHBjtDA/3AF+PgD99DTXntxKScxCen5/hUnd6vL15i+o/t442Pgyp92jqGNfT1zjfhTrb3LlUgKpa4MRBXBbjiE6/Awh4Yl0SVnGZU4yu1ltdElwvLLBjXC44DqIdusgXNuLtFxH0n2gEREAL8aeRxjg/8xpGmzcxvwjrRn9SxPoksr3P5bjyccvY8vTmTxqM4qfBrKBf7cr1Am+Q+uIy2TlGdzq8SZZ7UYS9MozpGY+JBowSYgHi+n4r1AymTxjBtmBh2kcvAQB7MHN3cBfKWEKVYNd7PbCJreCfVorJBlcbhMoFZg0qQMgeLxKEhUDcum3szvLLlfDMHzgJ8sSFovqK3RpEmH917Hm4myyst6iSpWHeoMpMlPGbqdBg5kkJ+cxe/ZpVq1KpFOnBWRnOxk/vg3t2lVi1KhGxMVFYLX6ZMF16z7qYSAENGwYzbp1A9B1QVpaIa+9tg2LRcVmM2G1qty4kVc6/vdasE+ceOCRLr1BQY+2y/F6DYYMqUetWuEsXNgXRZEZOLA2VqvK44/XIDY2nBUrEnG5NFwunQULzv09y/LfL+7ndP+e2x8Z/3E7XYDCYh/QGgKCAqDECZr3URGm2QzNE+AyTUkRe5GQCBOxlAsKJYR5lKEBmeIs9xOg6JLLZxCepZM+vQQMgSFrCFnHY89FxU6dsEHEOwdx2PMpsmEiZ5GBdL2Iqs/Z+LzmADSKQYattV/h9o0ydNPf5VjZWEYeyOJwq230qjKPVkTx+pPfELzJyr2ouixo9ATdHftYZXsVD6b7XBwIcUCYy0lei+kI+VvMwolGEHKX29R15dLA7OZYXg/MePjWGEG91OdZ1VhCuq+xtQiN1pc2sMtVFk0S3Er8GNbs5fFrZjrZVJo1WU2ypQrf5ySAkUOAfzV+bhrLiJNn8OxX2Ni/IyWSDU0yUdSwJUgSL/Zfy7ouzWgsqWxxvYjLm0PDPIU5GyoiOVTEDRnhAUc5hWXfdqYgK4kerW7xRLpBt/Z7kF0zAAdl/JJhh4Q4rVCVEpqH32P2J+uo0jYXeY4CxRKZns3Ua/gpWQsVTqMzMK0P54f8glTBixigk+M24feVjevBwdQtmIzZK9Oq+RvUOf4yF8OgNiaKb7oY+mIwPdsm8Oqoo6ScKMeE1/YB8NP8ZvyyqCNLl9ck7PwMBoWtB+DNg+2ZnRWMgPv0KImEhLLs2pWMLMOKFRdpXGM8YcZCPhgbz7BxfXyrTAi8Tg2HLmjRYjYFBW7cbh3DEFy/nku1atOZP/8JunWrzp49Q1m+/BIJCeWoVy+KgwdT+OijPRw8mArA8ePpyLKPfyvLPh7w+vVXGT++FTdu5DFnztnSeZ6eXky9epFcvZpTmqIwDEGFCgGlXrgtW5Zn//7bFBf7CndjxjR9JGd76lQ6a9ZcwePROHs2A0mSGDq0HvPmncXl0li9+gorVybSv3+tP3wt/7Pj/3a6f1CMexGGDYannoCLx+DqSaj7UHdnWXXz7oaX2FG+FuVpR0/pVwaKPQSYYjApNsrRHBUrUXoCCdpbVDF60s2YDYDzqn5fAixhBLg4PW40jeyv8DyJRBBPpF88ZrONu6ZjnBzyCrkxpyk84KYlH+FTKyiEX27MhLmr+W5+E945mkzl4jcR7X5BlgyCyeEZyzxad9xKxabhWJCpU5BB5WQPw+cUUTbNtzCyAwzWxAdwsXgow7TJfJW4icxAP4Qsc84vjM7Fk4jXrxB78CYzPvuQCnINep3PIPaeIFKXmHNjKrPeX067lsl0aX+dt8cdwuioIxkayRECWR1Kh6J+KMY9oAT0C7iFi6eHC2bUl2lddBhVeH2E52IvlHhRPIIltgU8YfsVFw6cJsHxChoU3oPnFsNGO54NFnKmBrHnYmWs58vyU/lcere5iVmfju9r0QQ3/eCkgqRJGBq0KJdK9W7ZqFYDucRXKA1RnVg23PAVAWWJK1JZ6q4azjvV6rE+KJx99yKpsexd2nz+DL2ffRpFEbhcTj5cf4FL93I5uO47mjX6iT27b/HahK4oUROYNb8h/nYNw4ALiSFcugzTpx9leHcLNpOGRdGoGZSLAPr2jWPKlE68+WYL2rSphK4buFw6mzYcwlu8AAmNIU9eIKaskwFPxTNtaldq1Ajj00/bkZ3txOn0+UeYzQqGIcjKctKz5xLu3CkkIsLO6NEJNGlSDrNZoUOHyrzySpOHpzjff3+CffuGlXJlfbLiCPr1i0NRfqMYCiHo2bMGa9cOfOTxr73Wgv794+jduybz5vUhKsrX10+WoV+/OHTd4LHHFmMy/YmvvjqCJEmlRjgATZvG8MUXPkaEphl88sm+P2bx/g/GA8rY33P7I+M/cqdrt8OMqb/97nRCzkNe0rU77Se8/m48ODjO53RmBqvlPgRSnh7Mvc/PBMmQqCuep+rZoeRtcOGNLiH0CSuyGQw3RHaO4MnI1b6L6l44sxTsYRTE3cZQ3Ci6H67Qe9hrmtB4krmYiZCu0eZOM2TNhCxU2t+OpM7da8inDC61tKMKjZEli8iVQugr9WDX5zYU11CyKmUSk6ZxqX4OL6eXZYXJBz6xlnN8krsYJfATxvHbbt4jWTEwo5w2kAxAKaZSpwZ0KbOVpVXOcW3gBeLeEjy5bzeyYbAv10N5r8LU5wwK/FScljtcM+5xQ42lmpYEludpnN6R5eXGsbbWCV4o+oiM7AakFZVn3Ped2d60PwmPZWIuGkwdw+CXg5/zWY2VtL51ijM946gu+mEXXqwyxPgVUSE6iF0fT8ekbgF0JEwQMAP0VLh1i0X1KtH70g48ZhNPfpRCriuYMHM+or0Oe1QuVw7h5uVpfLewBe+eH45nSSpX9AiuPP4YR771UKVmdYpCCnBmm9l1oDIjX3scT5GJVs3LEzqtLY5iF8VFb6AbCooisFq8XEoKZ/+RCuzcX4XFq+MxmxWaN4/hYsyL1MlK5MqVVL441QxNkzlwIIWCU9toV/YmzjrPluZIryQJbt4OolxUEflFYXzwYW9eeKE5AONe8fWKs9nMfPHFQQYPrktIiB/vvOPr2CtJPs7rgx1jSYmHzMwSKlUK5sknazNo0JrSQlrNmmE0blyWLVsG8/rr27BaVdLTixgxogFffdWFQ4dSKC72EBFhJzW1kMceW1w6/yUJWrQoX2qinp/vKk1JGAakpBTg729m9+5kNM1g2bKLTJ/ejcOHUxk/vtTbhXbtKqGqPtexJ57438deMICif4E24z8CdF0u+HkeBAXCkIG/kcc9Hnh6OOw5AHkP0SXTLsXidErY7TaipQQO8RElpOM0cll16gj+2V2o1/Ugmeopanr7U7A1EMMJnjQdT4bBhIwAtu6GT2MlRjW9f9G1b8Kx+VwLDOF064ZUSEgh1FSBpAFfkih/ispSLtOcEzQjsWkB3S9ex+IKpXr3aHKOPsWljBI2GlWopR5mckhb2rhPUjPNREiJYMwAL3vjArF4BJVu67yfeYHismeo7yjiPccPmNB4N+omLaU4TmnnCHF/zR2RgilwLVLT5YjdS3GrMi/V/gSv6xLbV0xi0/m67PKUwSa5cMkSS+0WrrodOCuBJllQhA29wMySi69RvSiBNnk/MPr5BrhMVg4b1TjlWk1r7zFibEncmNQC/CrwTNEczPf9g+MijvD18m0s/SSduJx6WIWHpIhwflndkIDyHpaveJyqFVIhHxAyFNSBwF6gjUBre5D19o8Z/Ox0JGFg8boxGxpncrpSpVkWot0gKmWtQlUEowae5FCvJ1i18L4ko34YR0b04qhVxW9bMUr1ZfTvU5PtO0zUqhWMuUxFrmXbKWP2MGfoJqadasKIZ06x51AVVm2qRds+wx+aWTojRmzAbFaIjR1Gfr6DuyW+I3lBTiFfdtjC8zt7cPzALR7ot3VdoUHHF6lbK4PziWWA3TRvXoW6dX10GofDy5QpBygsdLN16w1OnhzJ5ctZzJt3juBgK+fO3SMkxEqdOmWoUmU6DoeXDh0qs3Pns7RtW4ndu5MJDbUSEGChevVvqVEjjIEDa/Paa9vZs+cWV65k06JFBdatu0pUlD/Hj/ehUqVppW5mD9zDJk8+QN26ZRgypC6XLmWWvmNFkejWrRqKIhMS4ocsuyhfPgiPR6d9+8oMH76O4cPr8+KLTYiPj+T69bGkpRUSFxf+h6/rf3YYEnj+BQj4H9ENePQbMHuBD2SF8Akg/Px8lJCi4t9/THDZu/Tod4sFE5swL3k8hZFrubKnJXOHzUJVJVoOn0PfSRMJpAKdF2zFecV3xkjvaKfjIAWHAywWcD2Yrz/1JP/8CSqvS8Rp+FGuTiIfbh6GQ/U5l5fROnNzbxQ9Tq5lX9sKeJqnorGFWkTSXVN54cI80urdYYc0BAmDxkVX6JSSzlMbW/Lq42Hsqalh8sJb209Q0DGRrmIbZThD3SIHKbfKMyR6GmcrJ9CwsBlZIhU/bMy0/kxTbxIvuiuywL81brOFkqzqWPBQgh9j3QOoX24HuiRYUZRBP4/OaANmqZV5X34Pd807eDMBSaJGTC6zTxxENsFzgVPZkz+YskYqZwQMtoSTFLCattottuYPQ9FVMtbNIyuxCeWqteCc3ca+pIrMXtSAu/cCMZs1Jo6/wOsdc6HiId9X/x0Z7raFxseBEhxYWGrtwxt+E8g3hWBzO/jp2vsMiVwBcmUwd8NwzUFHZl/oEX7o/Tkbt1fD2ikcx+peGH5mYoRMqhRFtWrfcuNGHjabiUaNomjdaDE9WybRND4dJVTH6TLx3qReTP+5zl+cY7IsMWdOL4YPX+crZtWyk3H7LmnFAfxGoHtIOfgQa6BBgzL07VuLd95pyc2bedSvP7PUqnHF7A1UKp/O0DFPcDkpspTbO358az74YE/p9bKz3yIi4svSHfUDZoTFolCuXADJyT5T8kaNosnKcpCSUoDZrPDyy40pKfEyd+5ZDOPRDsOKItG9ezWys50cPZqGJPkKbz/+2JNevWpSVORm5cpERo/ehK4LvF6j9DmTk8cRHR3AkSOpdOo0H10XbNz4DJ06/Y4M9J8Qf0Q34OB4SbRe/feN3ViTf3034H+nyMr+DXDBl2b0ev/6Y/LTo1n6QzSLJsLhbyZz9G5XUs/VRvMqeDxw+2w8Ah03hYQ/44frho4aLmHWZVQF/O1Q/UH35rOrIOMyN7SGeNx+uL12bp1sQGxBW86FbcdcotP9s/VYi31KrtiVN2jTcB6nLCoyeazPy+XDLZ/RpvpMsINHsnHXW5e+ewI49GYPenjK4VWf5AYtmdyrIROLd9LBeRywIM9UqVJ4lx2moQx/fypOkUaOBELycMfxJTGBs8EPwkUO6URzTw4nwshFILE5egybPN2xn/+cl8tnMFYGVYLRWjK3NiTyfY4/AhUEjHjuJM3FaYp1G98UfUyIqx5CDaSadInqIpubhffYN6SEuPw3WPz6Ta6eddMvvAeZzdz0bDcSt8fXDsYwfIbmUbl5iA1ncT9rxmL1IPbIXLqbSu1GAq/Xgkn2MrhoBTUuX6Fd4/WUKc6me/JFKOMP9slcNdXiPX0uEWmC2LThvP9qCKfPRRGVeYf2Obe4ENGAT6WyOLQwypTxJz29AI9H4+DBFC5fasi4escQ1wUl8SaEgL2HoomKsiNJEiUlHlRVKXXDkiQYObIhLVtWYMWKp3A6vTRqVJYGdaZRIziHW0XBIMBj/Lacxo1rypdf+kQzZ85kcPFiFj/8cII2bSrQo0c1Nm68BmgMHNWTqMgiPvtgB0NG90cIgdutU6tWeCmwmkwye/bcomPHyuzdextdN0rnututc/Pmb8e4U6fulv7s8eh8990xJkxoS3r662zdep3hw9eXdvf1KcvukpvrKjXhuXOniN69l+JwvE9AgAWPR0fTfIAry77iockkl6rOFi48j8Ph+wL5+edT/2Og+0eE+BftdP8jQHfiB7B6A39myPxwSICigvZQUjz0PqNn3IsKm57ogMWAqnWgxCH4cFIKgbSiMa8jKRLJNQStycIFzDkcium0mU5tQGggLXsR3VtI1ig3sXknubyvKe8POEeT0Omk8C6FyQdRSnKRgDxrAO/1eovjplZ4ARuCO4HhJD3vz217FXTJAgLeWW/HllmNKi4X12wZ6MKEU7JioPCMey1W3DiRkWN0pEQFs+7luFSPiaIV66V8emJno/UZ7shRgKC29woj3YuwGoKFfq9SJLKIdSex194Gqjfmi8BCxmY3BkNHMtXny4IT3KtRjuVXY1FlgxitCI9mpl74LjKz7UgDdxPnKmHej1+xolIethU2pJ0XuO62MdYTxIHVz6EsVil2+D5kw5ABQZP6d+ha5jZPeE6BofOnlDeotO4E0WlpvLa/C4NM1ejcZhsNa21l0ao6TJ3RnOW1HifPG0zHW6MY8UJzxo5tSpp3PTHXJD5fqQGXWJnShZQ7QdzLsvPU7F1semkqhJynW99lnDmTiq5pWCw6JSUWXh52nLCuJUipgr7PPM3lWxHYdBOX93ckuGYDKP4Qo+Qr1m2pzIBRT+LnZ6VcuQDq1JmBLPu6HcTGhnN4VXNq7hzI7YIAwvw1oma8RHxcJvcyQ3jQLaP0IKl7uXevmA0bkpg9uxfXruVy4UImIJGVY2fL7tqlwGcYgrNn7zFyZAMOHEglOTmfoUPXMnPmY/TtG8eYMVvQdfGIW9lfCl2HL744zEcftWPIkHr4+5vp39+nNouO9ic724nbrWMyyRgPXczp9GK1qrzzzs5Swca0ad3weHQ6darCnTuFqGrwI3zfdu0q/o2V+u8Vf2R6QZKkUKARcEYIkf3Xxv5HgK6/vy+P+9dAV/Ao4IJvd5yZBf2GQGEhLJwFTzwOPoh+6v7NF/NwkHu/TLWyfDHLy9w389BBVGzKLf+jpNaReH7FYIKoxDMc4AabyWY9ke4E1terSp2000zpMp5fG7cvtUFzAR9YdIZFBCBLAl0Inj65Dk/gGQaMGcAyl42t0hDMpqpYXCGoNjdf+r3I1JKPKZRDueiNpAmXWBffmYyAKEZI8xFAqnaTD/RUvK5VWISbhWo/1DzBa5G7+KzoCcp6rzFKXkJN837unjPIbRvB935DGXt5O0q9nUjO1izsfpqFE4Ih9QTiXhJJe8uTOqgs+ren4WgBpwzBi5N78Movi2hbZRFfbd5NWIiD1ZviUM0g+mrULshiyvhdLF/dECPDTS/bdd6J9fmvegyFynfyeCF9EGE7Eom0lWA7uZ2UuA9YPhF+mNMIXZcZkNzvvtKqgNde28bMmSf58ptOjAiKwDokBc7IVEpJQpEaIEsqdepUhcCxYKrD5cu7cDrBbjVolXCbbf4deXnUaRRFIMpJjO5azI4j5fiq5g+YfpkJvSYjakxElgRd2ydRvUoWiVcj+eSTfei6wGSS2bHjJnfuFBFfLhqbVaGGkk9yfiCzp61jQK9LuDwqoydEMWpUI2bOPMWCrusYHHeJbbcr03PdQCpXDkZV5VJQrlLZzqxffyU5fSFHj6ZRoUIQkyYdfARYTSaZCxcyuHAhszRFYDLJuN0G4eF+FBZ6/qKBuNers3FjEg0bRrNyZSKDB9flxRcb07x5eRo0+Ilr13KRJImnnqrBpk3XeOmlJoSG2jAMQWHhb5KtjIwSJk7sQM+ei9mzJ5nwcBshIVbAl075PTXdv3MICdx/AAJKkhQCbAQ2Ad9IktRBCJH1l8b/R4Bu2Wjo1wuWrvrbYwMCfLJggOISWLAEUu/4inEfTvaBbhYXOGv8wp1jHajg6U2HttAdK99TggAex/roRZ9bTEDyT2D+GQUJJ7n8RCvSmMABxuBqaOVsw/ZIuoUOKWbg/uIwBIYskWoIjssfMZbXuXP7MWateA+r5qHDtcPMfmMuV0x1eAUb48jDq/rxvTKcOQxEt9lwvyyh6l50xUQlFNKEREfPblYVjEQFOgk3wWFXOf3V41TMTeNmWAUsg+6hmg2+sr1IhhoJbWQEXnIJYX/5pbRPv0KG4WVpqyE0S73I/LHrqJ60nyRXPgYS1AgEi+Jz3q9djWqiKjvqLyklII4dedw3LlBQHKTQ9e0mjBuxD2ZcBqdElr0mZy94yfP603z429T/9Hv2DpuJIgnOGwFEPa7jMSYiz9uArhtomkBRpFKnrcTEbF4etZxbJ3xHadHJ4JMpTQFBn2o36dJ3Adu2XedPf5pDw6gcCjI0GkWms/9wFZDTaTNwJEt/WMrMHxvjb+lImZINpBbYGLClL+rSq3z0eTVaN7tFicNM6p0ggFIXsNBQP7Ztu86nn+5DCLi6ZTHLv5jNN/sqcebtn7DZNHRDoijvKBUqxRFg8aIZMt+dbcyQ2PNUDMhnyZKLXLmSjarKDBwYz/z5TwAwc+ZjTJlygEOHUkuB9cHm02pV+fLLw6U7y4AAE8XFXiTJJ2Z4ALiK4ttha9pvW1BdNxg4cCXR0T7nMVWVadAgmubNy7N373OMH7+bJUsuculSFr17x9K/fxwjRqynuNhD9+5V2br1JrIM7dtXAmDbtuvouiAnx8n/Y++9w6uo1vb/z8zu6T0khEBooYUWQu+IoKD0IkiRLqAoChYQVEAUURAQsIIovUnvXTqB0EMgCSWQAunZyW4z6/fHhAjHI8I5fM97fH/vfV1zXdmTtdaePbPmmWeedT/3M2JEPS5d2o+Pj4UuXf4oWv7fDFWCAtNft3sM1ATGCiGOFRvgusCOP2v8tze6PyyB46egTYvHM7r5v2t8oKqwdqPm1xqNUK8443QTfbDLOThqb+WVNjV4o28Fxrxq4qocjB1BeUmPMAqNcyKBSzZwsup5jPjgRyR3OMZXYixJROKSquArpePADYPOTqNzFvwyJG74p/KbUw9lNX5kK/cGjOcZ0pyrAZCEilF1sc1QjSRXHvvlQoYaPZktCkGSKHRzp7Ikcw0VVWfgKP40wESFw2dpWvMAJmzogHmWPjzgh3BmAAAgAElEQVSbcJDKGUnohUqVjES6np/E7HoL2GJsg4oMEiiSkS+8xjLEKxDsdlq++jPJ3sEIScKl12Gu2ZppeLI5fwJbegQxP6g12FSOdypDK6kP6XtrYo6y38/dQLK8wV05A0V2p7LhCwi8CqPHgNWLQK8E2uAGXmuZ/PE16ngkI0uCW6UdjBiSjio9w+ie4/girwNvvbUTp1NFUQQdnrnCjv0RSBIEBXmD5AHCikPREXc7GKNOJSpcMz5du66isNCJQZZQhJGUPG8kZChSSLgRQKOeI7GnODHqMgjzrsm5dF/OZAQjSdDn1X7Uqp7EuUvB2B0WQMXf30Jc3HD8/d0ICfmipNLuxguBjN9eC0URTJvdjJkf7iTphh/7D5fD4p1NgcPAiL3PISE4lhrKzXwv9u+/jtOpSSTe158FaN/+F+7c0VZ+JQn8/S1kZRUVazi4HnqVN5kMxYwEiUqV/Ll8+S6qKli1qjsrVlxkxYoLgBaDFUJgtTrJy3Og02kUr/vqYd7eZpYvv0BWVhFZWUXExaWzeXMC+fkOVFWld+8oNm7sTXCwB7VrlyI318aoUTHMmXOCmjWDefvtxowb17jYc/8f1Mb9F6A+macbIEnSgyv93wohvgUQQhwAkCSpOVAf+PhRA/2tkyN+Owqvj4fvfoKhr/9rYzhd0LIZ6GRNDjI2TqDgKJngRUUSY99XCW96iRyxkvLFzylJkpB0EpIskcQW7nCcQtLJFYm0/zYTx93auIQO9yIX9dhJhDWB47N68c7BJny+Jp4Z0w9hbrkORh3G1HIL49CMb0K4zKAxH7HiuWcoFZTK5sn1yH6nOnfer8XZ9EsggYctn6ZJJ6jqsPMeHsSLABo4T5OuJJNzK59Vkp5bQLLkxo+5/Vi26M2SCl+rop5nZ4tuVA04iL+aQ4Ryi/t1vxzAJArA5EGqf1nsBhMuvXZzllLS6Jv9HM/blrN7dSmYcxE6l0Po9NiEkf6xjfhWhgS0iqSS6wxB1rUE5ixhw/K3uZ0eBkG74HoafHEFeeU5ZOvnpKYWsCm5ImmFHmwLMaHoddixsTV7CsM6/Uzmlc8Y3EeTH5z2/i5+27iIzybuYuTgdNKd+8FjBjr37kydeIBZk04zfukMQDNYsgwuVUYIMOsV+vWujH+YJ/IzpbGnarEmvSSoViuc24U+mPUKOklQt05pImt0xWQOwOFQ0etlXn+9AQEB2kLb3LnPExzsTsuW5Uq8PoC53zcmov7n1H1mJDq9J127atxVu6LDpuhZdbUGRrOZTz5pQ5s2EbRsWZYpU1r903lpMOj44IPmPPdcJe3aOB5+dc/OLqJ0aU9atSrHgQMDWLq0K8eODaFjx0j277+OomgGfcOGXjRoEEbFin6sWtWdSZOa88UXzzJoUJ2SserUKYXF8rv10emkYo9ZIikpiw0b4pkz5zihoV8QEPA5ISGeOBwTOXp0MEajrvgt4NEGt6DAQWpq/iPb/KdxfyHtcTbgnhCi3gPbtw+OJWknoBeQDTxyGf+JKGOSJHkDK9AqiFmBXkIIxz9ppweSijeA14QQ5x819r9CGfvtKLR5ARx/wVR4FEoFa3FdVQU3N5g59xq67u3JzTKz8cMJ/PZTb0ACSWXirkFMiVn8hzEyiGMDPQCJcgUxtPzoDHtL/UxMZke8bHms7zaD6o5Mqm6egaQ6sdEQodezNC6Pjbcq8+HsodRNnoESUBGP7m9gk8wYVRvxn7ShbOYdZECRYUmH5gxqtZipW2cy5uBibvqWpv74HWzNnUBz2zKKdDoa+mzivFqJsJxhGN0TqZ04nsXLx+PhKCLbN5waTZaQ28ofq+yBt5rHEOFins6P+5E7C1BIKDuwMZF8GmPAhuDV3HFE5a/i6trPqT4uA9WpwiuVCZ4fTeYH5ylnm8e6sMMEWeGn7sGML9MA4dBePXYdKM+7n47n9Onh8K432G1gAPqPJT1wAiNGbCExMYtr+UmE7liI0b+ALzbItEvWI492sGN/JF0G9qZx/WQWf7WexOt+dB7YF6PJl5RbwzDk+FJSMNLYHny2cfNmLssXHyN92w9k5ylMfK8xFV5+C4CdO6+xddkBbp07R2F+EQdulyXcM4+qkT6Uq3qQD8ft5eSFF2jfvWaJQXV3N7B0aVdCQjypVi0QDw9jcbbXMrZvv4Z4oOCH0SgzfXobJk/ej9XqRAjw9DRy+vRwSpf2xGIxUFjo5JtvThEY6E7fvlElamOTJu3j3Ll0QkM9EULg6Wli167Eh8IF/4ghQ+ry3XcvlHwODp5JRoYVi0XP8eNDiIoKfuQ9YLO52L07icuX73LtWjZjxzZk3LhdbN169SFVs/u/r3RpT1JSxj5yzAdx9Wom0dHf4nAoTJ/ehjffbPTYff8MT4MyZoyWRMDhx2ubank8ypgkSVOAC0KIlX/W5knDC32BL4UQuyRJWgC0Bzb+k3Y1geVCiHf+yf+eGmpH/XlZnseBXq9JNgoB7m5aiOKFjg62IeHpl8+EVnY6/wJ2RWCQBdUCI8klmVROUZY2WNAW04KoTWvmcIOd1NL3QW/sSsM7K/FUC5Bx0f3IIqQXpoNOj1CdmKRYpPo2hlSRGNIkAhZ1BYcVko9A1ze0bGFJQkFHZpAB3ywnQpYwVr6CHqiSnoiHo5DIjGu8m/0ZmUo6PXznMaBoFdGus1y1VGPgja8xHOxHa8+vuR4YQjm7i597zmJscABz1GzskokhRSv5xDIKIwa+wIoDMApoX9gFq3KCeZal2PbfxKMwntrWn8l1G4EruSMmFlMkqZhXXWHz0Ho0n32GjtFGIo0SRhVGb89g3O3anD3rxsvdz9LjhUtkhZkJIo21ZerS+OZpdJIEYaMI9vFg/cpgqtY4TNF1f27XfIsvW27luapnUYTEoNFdmDtjN6cPLGTf0bKUb/gmTrtcfP3yKUyfgLclDNSb2kV1aroD4eHevDOpHXmvN2fFsjgyKoRxvwzel18e47ff0tHpQrBaHSiKixvCi04Ngvn49V2YTAqtG67HxzuSzCzN07danXTtugqTSUdQkDvx8aPZsCG+xOCGhnrgcCgUFDgxGGQ+/3Q/3cNPsjQ+CslgoFWrciWVFKxWB0OHbmLdusvodFol4ZdeiqJGjSDWresFQKlSM0lP1wynwaBlzXXtWoW9e68TExPKzp2JJd7v6tUX+eabjsiydjNs29aXGTMO06xZOEVFLpxOhS+/PMrUqYdo27Y8q1f3eKgChtmsp2PHyg8phXl6mh7i9IL2dmcwSAweXIcnwa5dSTidKna7wo8/nnkqRvdpQOXpsBckSXoHSBVCLAF80FJ+/hRP9JVCiPkPfAwEMv6kaUOgoyRJrYDzwHAhxFMvjDH5E7D/wc9+fHh5QE6exnyYPhleGwFQjbYsICvvIG63QznQN49d141Et82lRbmhLKMpApVYvqIvvwHgooh9jEXBTrJ5BwPeP47XhX2w1ogQElJMP6jSFkbvRjq9ksSMy2yp8yrPla9PpSNrwLkJAJ3Lztab55kW4UawlMnH/SfjlnaTmhWWojMXke5WiglAc6MPQm8mp66FYepSwgNPYpfMbDK1JTLrCj7xWUxvsYalbQppVCkeIUk0f2cnx4MiMDvtLN88icb+sfhXnQnuAawvuErFhAQu1a5NrgTHDS3oH7eBHbMmM2NrU1QhM21gXboHZeNlhnVD67E/LpaXK31HjYjeTGp8mG2J5dBLgEEgAmW+fM+JqlZg37HyGGICGP19PuNUhbbDfmT61VO8GdIAfDSpTKxTGDs8h5HvdsDTU4fBL4JbBUnQQGHOmC3sOdaDOlG7GN7rJO273WLg93O5tegQrw05hrfpBKjvgrQFxA0cxhl88M4uCrKymdRXT88Psqhu3YZXyHUm32hNhr5CsfiLVl5m7NhGbNx4hV69qjN+XD0ObZ7GwRPh9Gl7AaG6UTEineEDTrH/cDm27IqkqMhFWloB6ZcvUvPIUH5u52T4nue5c6eADz5oRqlSnrRpE8GBKW/T33cHvStfIl7fkMGLNP/j9OlUmjdfVFKs0mSSuHjxLh06LKNmzSCmTmmFTgZ/fzcyMzWe8P79A8jIsLJhwxUWLerE6tWXHgo35ObaSUjIpEqVAJxOBZdLZcaMtsTEfEdBgYOGDUtz8OBNXC6VHTsSiYtLo2xZH5o0+ZGbN3NZvLgzvXpVf+je+OST1iQnZ3P1aiYGg0zduqFMn96GwED3Ep2Gx0WHDpWYNGkfiqLyxhv/HQYXQJX05Ot9/7ohAH9KRgD4FlglSdIQ4AKw81GNHxlekCTpGyDygV17hRAfS5LUCJgqhGjzJ/1igBQhRKokSUuANUKIP3jEkiQNA4YBhIeHR9+4ceNRx/oHvPkezJ7/1+3+Cvdfm+rUhK4vwquDYdZLC5hxYjA+RhtH5tmp0CWAbH0Ca+iIgg0JHcNJ1vRjyeYnolFxImNgIGcw4Q1FuWDLA4MZdn0GvmE4mr9GsJxBIQKTqpL+UVMseakgG6DKMzD0V5YXWVl+zcor3m9xwE1HUX4ApcodJYjbfJ+/gLNetQhCwtN1jeaOYyy1dMMumTGIImbe7cbCWR+QMOMcHzU4wFvRJ9BJgmZj13AyvCYWp53lP7/OC5f2Q5eZ0Gwk299tzs0a4bzR4yNckp4g14ckfLSMXnu7sflUJBICfz8rOpcgdut6QiNuQK6K9JMBglRELxd2l55fFtZiQMc4rAdNhH84hnynEbPZxc3YWXh5O2j7yiCOzXmDXyLL0lN1QMG75OZJnD97ksbRp7HZzJiCt6KztOTH+W/R6/m5uFmctOk+hENHQ6kbmMqezzZieS4KndgLxULz7DZAQii8dYx6rTdyOvYOOkmlSdgd3PROVj+/Bje9i1sFnpT78TWAEu/04sVRtGy5mHPn0hk7tiHzvzqEXdHhY7KTbbeQfGoWYSG52B16otsOJ/5qIP7+Fu5OPwqXtmF3yUw80oIvTjdEliXS0t4i0JSPfe9CjAemF08wHVf7x1G6Ujk+++wwU6YcBDTKV9++NTl9OpVz59KLZ6OKXhYM7x1KWFQN6tcvTYsWZfH2/hSr1fmHKsD30a1bFdas6UXLlos5deoOJpMOm02hsNCJXi9Tr14o58+nYzLpOX9+BOvXxzNu3C6KilxERvoTHz/637+RHgGXS8Vudz21Uj5PI7wg1TMJToY8XmP5xn8mI00IMfwf9xWTgOcC3R7R9ZwQ4n6Y8BRQ6U/G/xbtKUG9evWeOB/5rdH/vtE1GjW+LsCZc3D+klZdIv5sV5yqkSKXg7h8KxX1gfhSmRr0J5kdRPM6UnHapxlfmvMJF/mZGgzQDC6AxVvbvusM8btAZ0TxDMIa3ZJS2bcpn3WDLf0dKGZffNc24dSaWnQ89zz1Q2ZQy1oGsxhCR+dzuGQdF2I8OVc9BKePGeEF6QjS9RW4pStdvOgnqCydIoAM3rr2HWPc67MuMZL25RL5Ib4eP4VM4JM2g6iankjrq8cRqCib3kcqG0Nk0T2ePXWcCuk32E0XBr0+FuH3Gx/HHORCahAd2iXw5Uc7sBYauRAfROlKCvjIEKJClIJkALPBRbdXq5F65R1KZQziaK+fWHK7Ji+OvUigf6EWwnEVoLbYhPdPXaHRDIRtMSahsudAEzJ+rUrnyGvIrTOgtkL/ECvyVomsaG8OHCmNqkrE3Q0ms4qNsmL37xdQAEYF8lJhWnXiL70BgCok7E6JL5vuLUnSdakPi3dXqODH6dOpXLuWhRCwYEEsQtKjCgmry4SHhwGzyYVOBwZZZXbrnXS73oPMTLDqA/HQm5ARpFo1z09VBYXndqFu64+wO1FlCZ0scKoS7dv8iM0UyIoV3Zk27VBJSm7VqgEcP57ywIyUcanw9bI0HI6hGAw6FEV96FW/QYPSnDuXjru7gZwcGy6X4NChmyiKyqFDN0vGjooK5vTpVMaPb8yLL0aSnm7Fw8NIZOTX2O2aypmbm6aR+zi4e9fK8uUXiIkJpVGjMo97iwEai0Kv/2+rnSYD//mqF08UXpAkyQisBt4TQjzKLf1ZkqRpaK52Z+CTf/0Q/xxZagJmz2Bs+V48mPf+uJAkaNZIK8N+46bGZHC5ICsbRryUw9TF/nh6CFq8oGXaSEg05gMa88EfxqpKb6rS+w/7AU20U2j8AYsqWJmWSrtZbTGoLhLq6djTOYAhUxdhc1iYfspOfN/Z6E2v4yYuIIQOi8uBx1UfTof0ooLrJokBZbHpNYKhHVNJIcqLoikNlzrJNV6kfSkffnxlK8MHfcpvzlrc3VmIOTGWaV1G8VH7MYw6tISPdszmNetNLmx/nq9i1mLLvMdrL6wk9J2JICvUaesi+bWvyFDdMBpVFNVJ3ag72qKRsRpUSoAzAu6AWk0wd10Z2jcNJVwvUz0wmykxt3HVy8SpyuTnGtizP4JNLyzCtSsZGpvQStpIhLgV8GK3eGR3FbZqBer1x1aCQ8LLWoE2bcqzb28SdUMyCAvJ+4dzK0HyfYWjAva8dYlmn1akSVgKP7bbRVnLPU2Js5oC4Q7CduSQcscHf38LCxd2JDjYHXd3I6oqeLFjBVplzmLFlaqMqx+L3P1LBr81jA3vz8GQBE10d6gffJtDaRWQu30JlethU9zZ+P0N7i9YP/PSMfqWj6FzhQTeOPAMMWHZ3LWaSM6yYLHYkCTo2LESGzcmoCiCzz77raQ0++8Q1ChvwGDQUqfvsxFkGTp1imTp0q5cvZqFn5+FsmVn43IpZGQUUqbMLKKiAjl7NgM3Nz379w/AYjHQtetKZs06BsCzz1bAatXYOc2bhzNz5rMUFTlJTy9g9+5kNm6M5803G9GwYdgfpnGbNktISMhEliXOnh1BpUr+j7i7/g6QQbj9dbOnjCcNIw9GI/5OkCRpArAALWbbRwgx8YF2HwPL0MzBRiEedE2eDhzCSoc+9mKD+69BCDhyAnasBz8f+GkZnDwDH74HLZpE8vzLsPBHT7bshIF9/42Dfek7sg+P47eYRHz942l00o5egMHlJDLWhc+5fN5ymXEJAw5V5W69pvgn2HGz7kKSFfJM7nzy7OsMObqcWrcvMKL7NG77hnA4Ihq//CwyPbXJL6sKfrddhAVkML/jVjYObMvGwGcprL+DtfE5GguiGRBm5stWQ4i+eZbXN37MT56lqTv9FiaTgnAClwyQK0GCjKinsnlNZV7ucQ6bXc/KX6tzKi6MKTOXENJkE+wbDCkgnRN8Od9Fw5YjUF4vQLdHwnjhOjv3fc+vm9dx5qgP1wbPJ9zdilCug/kOEj4kXFqB0V1FF64iZHC1FThdRvQOhTVXqjFgTkeM5hSee74yi6e0QedWD6TFYDsFOgcYo8BuBW4CEg2s63BscWnsiCNGuCcw6ARSaUFE7Rw+n7yTAa+9xPLl3ahWLRCAxJOduHVoJ5Fto5EXZjIsegPoTdC1Ie1eegZ+yYKzy7HoXYyoc5F50z/F4ukOTYbhBXzwwWEmT96HzaZw7a6FGdmNmH8umrtF7hy9W4EXX6wMFy5TVORi48YrNGsWzpYtGjMgK8sGaA6AyaQjKNBCRIiOuCs2unZdyZo1PVm79nJJ8sPatZepVu03Jk9uQXp6wUMecGpqAampGs83M9NWHKuuwc6diSVFKrduvYrZrEdRBKNH12f48M3ExaUV83c1atr27Ynk5LzzBxpYamoBdruCu7uBjAzr/w6j+z/g6T4RT1cIsUAI4SuEaFm8rRRCXPoHg4sQ4oIQoqYQIkoIMeHpHrKGe7k20hMqUuzm8XBdiCeD2QjVq0JMNBw7Ae27aiGGPkNg0VJNxez4k7DZVAWWDYEpkXBuA3iVYs9zmaQE3OKytJLhUXYuBkVQpDchuyRKF+Yy9YUJuNXJweezFDb1r0t+SC9k/R4kIfCUTYyt2oW2o5YROPU0a+p04GjZOghJptDszpv7vqV66hVe2reBpHvlkfRQWFkl3J6inZqEHITVhVFVCEjOxx0JH5eTbud3UjstnunNDlJ414SiFAdM7lPwGgkwwuFTZQir+xbl64+hZZsUFny5hbiiAahSs5LTrrokmv7oSaOaSehMKq5nBEKSiO/Uim2ffkradG+8/AsoqqDgqqrAZ7Xg1A5qVbtG/Ya3GfB6Fxb+XI/vynWnzwKVqdcb89mlhrhUGZvNzpYt1xg7KxP8h8KpDjAT+NYLDINgeAr4FRsIIWCbDrbqwCFAFkh6EOW1hacriRW4detN2rYt5jK47Hh80wy3g9Pp2fwjGq4aRL9tzzPfcyGYiheMOn4COiNXsv2YebIu1Wt8Q2TkPHJzNYM5fnyTh163JaMFc0BIST2z8HDvkv/NmXOcfv1qERkZgJ+fhR49qmE0apV2d+/uzzvvNufAiVxyc+2sXx/PV18d45VXamMwaLeqomi6DADBwR4MHFgbvV76pyye++3efbdpyT69Xmbbtr6kpr5Fjx7VOXMmDSG0mOt9epheL/HWWztp2XIxsbF3SvquWNGNmJhQRo+uT+PGTxZe+O+EDLg95vb08LeVdlRVMAYVoTgtf934ETCZwGyCtq1g2y6wFmr7XxuufU5MBosZ9m6GBo8bRr+6H74vpoG5+cG0VLbQjxQOI6NnATM4Q332zu9Dy6uaEtWF6s/SfMg3uCOThcorh5YwY9N0TC4n2Z7+eA9ciV9EOaxC0P7SPtL9ynE5OBSLzca1Kc3xKSrArhhZf+tF0kzejKz4Aw5/wR23csTdK8P782rTPOgGs3of4dzIg8R4hWOeVBbFlo/QG9BP3IusbIDY63AlA+x5EHgC0cJBZr6ZZj2G4vVaWfZ0mYQHhTjRsy/5GZ7N3AmXQzld6kP6t67CYX17dEIluagMY9TPORwRjQOQVRdNb5Rnd5GCYZEBXBJCEkjjnVRrNJJREbF4mlws7z+QH49+ineDTNIqmnF3d/LW5Gepl3mXxOpvM/frTjAhBAqzwOgOr5UD4xnELQnW6ZEKH5BZlIDh3qB6owQ253ZmRfzD3npoMUcUZjOpVS9SCjzYdr0CGYXuCCT0ehmn8wPOnk1j6NBN9K16iU9/dSMtT+trMMh8/fXzDB0aXfx5Ci6XitEo88MPnWjUKIyvvz5JerqV3bsTycjQJpbZrOPMmRFUqaLpzwohEAJefXULv/xytkSx6z4+/LAFkye3JCUllx491lBQ4GDVqu5UrRr4ULslS84yZMjGEv0DTSOiHy1alAO0kjvTph2iTZsIRo2qX9LvvuylLEvMn/88Fy/epXJlf959dzdWq5Py5X05dOiVf1pr7X8ST2chLUBwvMPjNdYveWoLaX9bo3v3HgRVeFSLh/VN/woPKkIZDHB8j5YsMWM2NG2klf95bGQmw4y62t+hNWHMAezkcYlleFOWm7RmOvmsmN4S34yr2qtszwUQ05dG3CXWZSX61nmev7SPMjmp1Lt1jhqK4GzPr3imfDWsLTZTdDKDNkP1/Bi4gDI56ZqvX1yx166YsehtxVloEk6dHqdRh8fgPO2hndcStjrA3Q8qtYFq7RBB5chVbuHtDEK6GQtZ1xGrRhNn8GfUrnYc9aiPZWsLzjg6EKHcZJXpRaKc8dRKvYw908i8JreIMngyznWJCupVNhsa4JSMSIBegK/I4uf1LzLmjec51XkRbiYXkkEgxjiZM6ARwyvHodep5JXW45fqQFRQkTorYAC1QEKaayA+qBfPzKuNNSeXLZ1W0aR8Lrz1Lq6743BlqBzaVJ6G3rl4FuaAVYCsZ931SHSNi3ix7xUkfQj4nQb592SBhAs3CPy6JgZZ4W6RhQqLRoIkEx0dwsmTw2jY8HuOH7+NxaJHp5NK6oiBlgSxZElXevWqzujRW5k//yS1apXi6NHBmM160tLyKVt2dgm9y2jUsuP0eplvvnmBxo3DaNToB/LzHXh7m0hPtz40Hzt3rsKSJV1KUnbvw+VSuX49h3LlfErSiF0uFW/vTyksdGI06ti7tz9NmoQ/cpqqqiAnx8bOnYnUrBlcEm45fjyFVq1+wulUcbk0SceWLcuxceNLT4198O/iqRjd6CDB8UfxAR6AYeFTM7p/2zTgQaP+qsWTLaw9+OwZNgAqRGgVhS9choYxkJSsKZE9Fvwj4M0j0HMB+cM3MZMCfsVAbYZTnudoiYkdBODbcyEisCJUeRZqdgbgQzzxFoJ1i0bi5bBSLvs2NdKvQeZ1an3Xk9+2HEbE3gO9zJ6TXnjl5CEhoSIjkJAlkHW/czhdsowkBPeq1QKTBDpweR2mVbexTAmvhjBaUIPCae3cQxmXIPPTqoiFzyNWjya90J2kSz7EngvFcjYd07VsqvvsoZdtDrXPX6TWuXjEEj2GrVDlpwH4XNzB2fFNeG/+LAJytfpI5bNuMenaCo7efYF3Jj9LfEogDVcPYm9GONgkmKWnT8ULGI0KOr2KX6gN/EG6pxko4QApTbuaP28tIjU1n9xCmel3x8IHCSB1Q1lgxrXChPOKjs57PsM2NBY6zSAubBQvb32e2q1ScSkSH3xSg1cHfU9mhnYhBQKn914sBieXsgKo8fMwQMKoh549q9Or12pcLhU3Nz2SJPHee00fuswOh8qvv14GYN685ykoeJ/Tp4dx8OANxo3bSUTEVzidaknNModDxelUKSpysXVrAsuXXyAzswibzYW/v6WYWeDPq69Gc/DgK6xb1+sPBldRVOrX/44qVebh4fEJH3ywl7w8O8OGbcJm0x4IsixRoYLfn05Pp1Nh/vyT+Pl9RqlSM5EkqcTgglb/bP36XiWLaaoK+/ffYN68E495A/xdcD+m+zjb08PfUvDG5YLrN//fjT+ov6bnsGMvOByCkV0Os65lN/odW8bcDW0If5xwVqmqUKoqg8hiIzb0aNSyTvweDjlcYQ/n3ssnNPUCHd/3Qxf9Mu36/MBdQwTX+n5PxKE5fN2kH3c9/OhxdhsoDiIuzKCsf9w0n8YAACAASURBVGuu/DYIOchMi+wqxM3qTF6vrxkcHEr/3fOIqFyVwrDLWGyRVP92DjqhUDbuNFSRoIxggXtf9ns14kSpWjyzdiqla1XjiHsNKqUl41ZUqHnNqkqQJZ/zmTWJm/ItRbVN1LB8TpPwXsx9fQed+3xHvsmd1bEjqXkngbaXDyBf2g9CpVPPOaT6lEJSVd7fMZdXUlbi7KXSIPoWl68GcjXTH1Gkp8il54bZgzMRgbwQdhUPs4KopyJJ/nAyB+lHI/irkKwZrdYtwpgdq03ZF7rX0WKu149hMOgwYaNxaArdF6fQoqeD46ubYtjWlytHUgnwt/Lrtkhmzo9BVq30dTSkabQX13q250iZZWQ38WHRtGgKXZqBa1LqOl99dZzbt/MxGnXo9RKRkf706RPF5MkHSkTA3d0N2GwuSpWaSf36penfvxZeXia6dFlJUZHzoSoP93E/ayw1tYDhw+thMmk0tlGjYhg58vfX/j9DerqV8+fTURSBoih8/vkRUlMLWLw4DiFAp4PFizs9MoFh2LBNLFt2vsQDnzhxLwkJmQwcWIsyZbT4c7t2FQkKcqdBg+9xOlUMBhl////8Sv//W/w92Av/4xACmj8HFy493XElSYvtBgZCjaoahUzWuTCbHFT3PouvKYd3qnzEpu1tGDUUcNrgzCrwKwsVWyBUTXVM0hffYXYrbP+YbhSxrf3rqCY3Mh9Y7BMIzvEDSIKMgAKyQvQEnloG3b4Ckwc/RzZiSuUaCEki292XHtdOgDUL272GbH/pLY5v09N/qJ0LIZWx6vT4lK7N2tCaMOgZFlETG9mUun6amkLVfH7FCUt1MEplvt9A9MKJkCR8rh/HPv80kWM/52pQRX7LK0tr0xWWXalO55gEJjQ4iiFLgRwV1dfAonZbmV93IHGh1VBkHR+0H8uKJa9jdjmQAEWAPdUJ/gpCFURk34MuLgwyzBu3jdidobzXKJZnwpK4balN/TntsRZJuLvZOX9gIfrs6pQ+owncTNrSjC/PNKCsZw65DjNjWqZz8eIkiopcv3tm5Rsjh5VGuXWD9w88Q1GRi6RzVwmrfoUvh+npEZKHJEPdGrlICvSqHE89/+uQomB97zY76tYkveAeSy9WBQQ6STCmzgnGx9dFljWv0OGAhIRMTp9OY/LkFvzwwxlGj46hefOyNG++CJtNYdOmBPbsSWbEiOiSOO19PKibcJ9tcPLkHZKTs1m7tidly3pTrVrQY83TkBAPWreOYOfOJCRJqw5x8WJGyfcpCsyff5JOnapgNv/x9o6NvcOyZRceymi7di2LSZP2MWXKARISXiM29g5Go46OHSuTmTmeb76Jxc/PwsCBtR/rGP8++BvwdP8bkJ//hEyCx4DFAvM+h8oVISwUTsRCx/bw/i+zuRefzKfJi7EJAzvuPEvN+/fG8qFwQUvfVfquJ3VjPZR8gV9XM54NjbBjKhyaT09ACb7H7YYqDegOdAc0zm8YTUgTpzDZ7PjkGKBMdW1xCOiChS8kK06hMsK3Cjz7Pmx8jxzeQ8JCnZtO6icJamQsx8NRCHHrtfgxYC7S0/HrLLwzXDzM7JDhZz176MuSRt1okBhH1YwkMi3eTLv0Cheql0Jk2ZFDoU/kJaQCgZairwNVxWGohT4glzoplzApTnA5iLp2AYvrAZ6pgHavL2B5k248dzeW6qWOggUkA+gCBd+/U0it20nggpCi8/zQ2knPTZ3ILzBTs9mrnN09H/QKTsWNqSea4mG0czkrEIHEe9u8eDXQ/eFX7uwR0O0CkiqRtC8cWYYCl5l7Nh0jF3agx9iLCAXKXM1kYtskfG230csqhU49V7N92fZRNFW6nS1xR5uF3uTFfm2Iin6ZefNOcOTILc6fT8fpVLlxI6e4dllzEhIyiYn5Dpvt9+wwRVGpVy+Uzp2rsGXLVYqKnDid2uKayaTH5VIpV86HmzdzUVXBxIl7ycmxU6mSH2fODH8saURJkti+/WVOn06lfv3vUVVBbGwqjRqFcfSolmRx6lQqn376Gx06VCImpnRJ39jYOwwfvvkhsfMHq08oimDy5H2sWaOFTGbNasewYdG8/Xbjvzyuvyfusxf+s/jbGV0vL+jeCVat57HKlTwOXnwOUu7A7v2waZs2ZulQqFjtFeq/P4C1PuGsHTydIr9OTHiuuNO9a+AsQhgs2E9fQymMBgF5B+ya0ZVkkCSEDNaYI3iicJhTlKUJHoTAmdV02HaW7AbN8Wo2A8PIVNTgysjFN15tDGQQjFMC78DS4FUOzm/ElHwcO40wO13s/6YpOjUDdEaWR7/Ih6TTGTMfnO6OJW0qOgUwe4OtWH8jJApSzxHKXd7dsRAAYXDD3Wmj9VKZ+Fb1aFP6Z2RAQmgeslGGqGZgPcK9rfd4eeSXzF41iXd2LWBOxe703rtOK6xmMINTq7X1UeVdfFO0EZOnk9wsE8c2hFGv422ku9HUem0J7JiC2DsTWXHyYvnL+IT1YFq1XQxveBid0wn9BHJ8B2I2O1nf4huiVg7VUnO97FjkPcBzv18821kwgawIrt2WtIoUioy7wUGU/13uzPaltG8+Vy4H8u2ZqjgLy9Cl4lUCLVYOplXk2dbVeXfacK6d+4zUXAPfLn8b6lUnAvjii3Y4nQo9eqxmx45EJk7ch5+PkQEdvdi8MY2ioofl7UJCPLBanWzalEDNmkG89FIUHh5GFEWlS+R1/Ha/jRJWl7VuE7B4utGjx2rsdoXz5zOwWp1/iN8+CmPGbEdVtQq/vr4W9u0bQJ8+69ix4xoOh8Jnnx3m88+P8NNPnenevRrffBPL2LE7cDgUTCYdsizRqVMkZcp4sXnzVeLj71GzZhBOp4rN5kSSJK5cyXzSW+lvBj3wuNoLT/db/3ZYuRh+Wgh5+RBS+d83vL9u1rR0H8TVRLia6M+hvZu4dRle3nY/bFAAP4/StBJKVcPhqsy9+BdBdYLsxL2Oj9au3QSQdRpXU16NQgEgoaP4xlo+FNlZhP+OVKg8iq/LVGYM96iIjmME4oOM2wPrnHdMFu4584hS+lGkbwAxtdE1Wgt6M7fNbvT3lQgmnjmiLH2OraOWogASmD1/N7qp5wDN7x3baQJ7KzVh0w/DKJOdgoJEzeRE7oVEUupuEpJOr8mwdZgCa18HRVDa5ybHW3ZBGahjtUcXrHIgdyPLQlI6OIuLOAKVfLTvS8n3pMbPQ3GpMh2/SmTFK5ch8TXwDsMV4IU+/R6mxg4Wf7iPF6Ye51BgA0IPp1Gp3TV2HPNkc6t5+JgcnFuxkEO3wmnTOAkdZXjI6Pr/ADdaQq4dp8uTDS+swqRTia/6Lu36jWFCH4Vvmq5mzvnG3EhTMemM9NneiS2dVvH58+cxfLgGnU5mxak5kHMbMpNAcWkF9dB0bWVZwuFwodfruL1iBlzaxgj/KD40dyiRdJQkre3IkVtwOlXOnk3n/feb0aFDcYrtpC6Qn4YoyKJs9XbE9B5Mx46V+fXXeAYPrvtEBreoyMWRI7cA0OlkNmzojcmkZ/nybmzZksCCBSfZtSsZgGnTDlK3bgh79yaViOy0b1+JiROb06CBtlA2Y8azJWPfuJHD9es5mEx6xo//3+rh3ocEPJ3SEU+Cv6XRBTCbte2nBdDvDwoRjw9Zepi58I8osErUbQqJ54rfQH9bCGfXgeqCGh3JuPkdQgUJK/6mj3F/Zp7W0egGHT5GBrrQlwR+pSytsVCcxeNXDrJuaIN6lWIaBShACiq7sdOdh/nHO65up3n+PWx6GUk6yd66ibQIH4cHIezJu8oHygC8dRncE6UJzE8r7iWg2yz4oQe/hxgk4mJ68W2TlxlwfDWB+ZpQnIygafIpcA+At09CQAXN8BxbBOEqhAhQBZKkYkRleOFSfvToS210v49tsGixY9UFksRZRxAuWcLqMLL7ZllIXw8ZCaA3o3Yagq38HNAZuJYVwRc9I5kb1Y9MnT9xX3bmOecKJDdQBYTGFdK782XwjCLuynPMX7CJTp0iNYPmXg+qaVlYe76aTdjxm5hlB896z4EqA/j+xCKUfXX42jiVdmGX6bW1CydSQ9l+qwpd2j0H9yUOs67DjGhtMlRrDwOWlZz72bPbU1DgwNdNYXSZWeCyY8k4zcXYFVh8/ZFliYEDf2Xz5gTtNBi06gxRUcEIoVV3oHRNnFdycdhcDJsQT++0I6xZ83sNPoA7d/Lx87P801jsg3BzM9C7dw1WrLhA06ZliIkJ1aacUUeXLlWpWNGP9u2Xkpqaz9mz6XTsuIxly7qxffs18vIcnDhxh4iIf+7hlS3rw5Ejgx/5/f97IIH0n6fA/W0pY/fxcm/o9yeSB48DVUCnDhAYoIUrJEkTwXkQyTcfKGrpGQyyHnRG8C6NVwM7CBWdSMViXQdFf5TS9COShrxDiFpXMzouB7y2F7p/BWMPg3conTBjQXsKNij2hoVLcG9FIalz8un97VQqZN1Cp6p8+soLyIrAPK0x/NSHVglbCJJuYZTslBZJ+CjFxUj9ykGNF2DcSYjpB+UagSwTcu0wEhJpnoGApP0eJNydNtxzU8G3TImnR+Uy0M0FTRVooEPoDAgVAhOzSPqiJb43ToLJC4we0H0OBBbXpQ+GVpNSqF71LmaTk48bHdD2Fz/hTG71EdsacGtdJd7MWMWocj9wtqAtwWo6JntBCe/YiUyfCqtJvLcLcecNvh82kdVLDtO9+2pu3sx96DxXjPDGrHNqv6dUNUDjxJp2TsKo5NO+XBIxwakUqSaqv7NQ8+Lv48557QsdVoridqDOaYW4foJt266SnJzNzp39WLmuP15VYxDA+muRVI/+hX37rjN16kECAtywWAyYzXrefrsxly+P5PXXt6HXT2HQoA0waDXLpDeJWTGY82lenD+f/tCxv/vubiIiviI8fBbp6QV/OW+XLeuG1fo+e/cOeEgbFyAqKpiVK7tjsRgALdZcu3YpvLy02n5Wq4M9e5L+MOb//yCjebqPsz09/G2TIx5Eym0oF/XoasCPwtzPNdGbL+ZqoQo/X0305j4+eg8+eAcGj4LVvwq+GbCaPh2zocFA0BkRy4bBmRWabm6vP5E9EwK+bgs3ToJfOIyLhQdUlwSCeHsOZQ99h5tXKVAUCtYfIYtpCGHGwHlCXa1x6QysnBxB1y9TsOQUgtEd0elTdnpMJqmmngpnbLRdkock6eCVFVC5NegMWgLGzwPg9AoA4kNrMLLTu5idNirfvc6knXPxc7ngmfGQmQgXNmt/l9GBeQwYtZ+gFid6yS4gRYIVJohoDLdOgrBBVxfs1IMLGK6A0QJp7rCo+GEUXAUl5hWyogYTGOAG9xJBaggimwLceF+ZxLQjqXge/QEhYF1iZdykIlqGJWPWqzgVmYuZAdRfNQw3NwM1agQxe3Y7UlLyeP5CH0xZl7QH4kvfQ42OMP9ZuBmLSzJQYJOotHgETqMfOTnvPnx9HIXkfPYMy/dDvyrn8DA6+fZSA4bvbIMkQUCAtuDSoUNF1q2MI69Ixs1Nj9OpcW8tFj3z53fA399Chw6VaNNmCfv3a5pQOp1EZuZ4CguddO++GpvNxYQJzTh7No0ePapTo0YQwcGfk5FRiLu7np9+6kK3btX+tcn8ABYsOMXRo7eYMKEZkZEBTJiwhy++OIq7u5Fz50ZQuvS/rlvyP42nk5EWKTi+4PEa69v8X0baPyI1DRq3fXL+rrcXbF0NrV8Ee7EY5YMLdNUi4YPxMHEqJN/Q9ssy5KWA+5OwTZw2GF+cg683a95n0D9I6s2oB6nn0V57ZGyiAS5CcGMzNqkZbt5XIPc2hNXRFshuHMOul5j/TgxYMuiw059Kuw9xvbqRC00sdNhWAfnOec3zq9WNggpN6errTmJAOD8uG0enId+Ra/HCw1bA/DUTichJo1Gt3ug2vANKMSPBOwSq3UJUUiEYTcegOI7JPeA7I5SuBbfPgk5ACwUKJDihA3dB7LhlXMrxpe/C3siSjrz+m6n13GFu385j+PBo5s59Hgq/goJxoK8NvvtBcoOCuziPLcW5YQImWZMhLKa4UiTMlFv2Hhl37VgsehRFxWDQ0bZSBuufWaQ1GrkDbpyAje+CUFAMXrx2ZzqbD+bzxRft6NGjGnFxaZw+nUrXrlVRFJWwsFlU87rFwR4/o5MFA7Z3ZNXVh8W9ZVkqoX1FRPhw+3YeDoeKyaQjI2McXl4mMjKshIZ+UaJlEBrqwfXrb5SohmVnFxEWNouiIieenibi40dRqdJcrFYnbm56btx4s8TIP4iZM4/wyy/nGD++CX36RJXsj4+/R9u2P+NyKWzd2pc6df5cIzYlJQ8/Pwtuboa/nLL/zXg6Rrea4MSSx2usi/m/jLR/REgp6NPjyfvl5sHAkb/nr3m4azzd++ydpBswaLSmwSCEpsNQqYJGM3skhIDzGzSPUQhtdT/6Je1/ZWO0mOk/Iu3i/c4gFMwcwZ11yNixiN2QcwuECrditdI+TV5l1Sv9kDyTMBvusb5dLt99FsD2IT6klTfgcmVpMVZnEZz6hVUZcRyq3IQk/3Be6TOT4YeXolNc+Bbm8WqPabQf+gODzELrU3KCUuGoHpYYkfbIiCsSXJbgpgS/FocganXTnkD+ElSV4bp28i761qKZV2MGl61KzCcXufbKRbbGmbl3rxCnU2Xx4rNaf7cxEOSAU13g/bKaR+7mj8HDC6NBV7JQBRL4+WPpXkS7lqdwd5dRVYHoFoG1ZwRnsstorBGhwtHvYPc0kFwgga5CQ+aPsXBzuTs9ulQkMTGLJk1+ZPTorbRt+zOKIhBCcDojhBc39mDikdbsuFEe0AytyaTDbNYjyxJGo47Klf1IShrDunW96NQpkrVre+Llpb2GBgS4ER0dgnw/XJxVyMyZR0tOqd2uoCgqQmj1yU6evFNCFzMYdP/U4CYnZzNx4l7Onk1nwIBfH6J9zZt3gpSUPNLSrMyY8eiiX2FhXn97g/v0IAHGx9weMYokeUuStE2SpJ2SJK0vlsD9U/xtF9L+GQIDtAQHh/PJGA1XE6FcuKa1oKrw+RSY+jmcOgNIUKY03Lqttf3uKy0GLP/V42r/bNj+sbbG9MIn0OxVeHkx9Fqover/M05mheaQeAitkwzChVS8SCXpTRDRFK7u1f7vssH+2VTWd+dkuIpDNpHnDKdq2j3uBToISAOajoS1EzRmBVDt1nkkpw2zJHHdJxR/vYmsvUvZplMZ3KQnVpM7+yo2ALOABi448Pv0kABO65FOgxYMkUoeVOybBZ9kgXJDK4veNQ5SL5BerxuyJOFEkLzoElGjDgMCb28zNpuLgQNr/f7bVQW2faT9tvMbID0ehIQe1+9PRIMJhjlBcrJo9joG9ffn18gJzA2XMAoXfbcvZu7cmgSa8uhl2IyriZMTBaWoEpCJr0PCtexVhKpSkHCBlPJjkSQoLHSRlJRNUJA7q1b14JdfztGrVw8WLDiFXb6FxQK7dvXD39+NnBwbQgiOHUuhd+8aAHToUPl3hkIxZFni8OHBDBr0K8uWXcBuV/n66xPUrBlEhw6VKVXKg2+/fYGvvz7ByJExtGpVjtBQT65dy2LMmIZ/mBaKotKr1xrsdgVZBl9f80Ol21u3juDHH88gSZpe7v/hcSGB9FTitY9bOxL4X2Z0Xx0Mt+9oxnL/b0/WNytbE9GxFsLwN6BjO6gVBcMGagkT6zdDvTpQs8ZjDpger4UUkCDjyu/7DeY/7zNii/aa7hEAh7+jKHYZpoJ7yBZveO8cWHzgyA+w5jW0UjUKVa5cI3rPHRwGI0Wj38GnTHXUz2ujz7mL5PUtTEqA06vg+jEaXtjI4Tndue5bmjUNXiKm5Ti8rsfR4fsuRFaO4WxIFTxt+aQ8G0BY1VTI08OZ4hVESf//tXfe4VFVWx9+98ykQoBQEkjovUjvUkJHkA8RFWwoIKLYvaJYsKGiWBFRFCxIUeHCVYqC0ouACEovEUPvNYHUKfv7Y81kJiEJCSSQhP0+z3mYss85+8yENeus/VtrgbvNnScgpZVGaQWJZ2FMI7j7G/6sUI7ztdrSsUQEHddMYfv2eWwrVYGPZ97IDtsZjsQX4/77GzJ8+I2UKeMTn7FYIaK+xHht/jDzEdi3zudsyB3DuVgIBatF06GGZmaNYlhcF3BpCz9+YSFmRXusyoVqEsKkd0+wbmMgAQFO5j/5N02dKViVZv2iP+k+rRKfjz1CtchFWIpKfLd371r07i3dqbp2rca0aVuoXbt0auEYB5qJJODX2Ebs3Kk8PUVRt0VdRo5sn5re68Fms/DBB93dVcb2cvjwefr2ncn58y/g729lx46TbNt2kkcf/YWmTSPYtetRkpOdGSoXDh2KY/Pm46kfwdKl96c5X9++ddiwYSgOh4sGDbLu/GvwxePpZovSSinf+OdETxv2HPSOBApReAGkTON7b3rb72SFxQID+pNaRyExCex2US7sOwDjJ8GXUyRpIjQUBg/IgcEF6D4SKrWEKq1lQSo7WG1QsSmUrMTQHk9Q9JUVNPrPTyTZE0QfrBTc+ICkHiMdgw8lx2JzubDZHZTYvRJr4gX8Th5GpSTC2f0Q8zv8/DLs+AWNovHhHfTZtohaR3bQAj84f5yiKYl0il6DQrMrvDovtxgOlkAoVcc7N0Vqthza7eVWcUkJsVYOKLKdOb+9TAfHEXqnHGT0xkmoBa9T6cBf3Pz3HBbWHkH04C9o9Esdvn+jHmtce6TWsC9PLIdBM6DJnbD/D37dX4nYZH+vpM+RDDMD0Umg9ykSP5/O6/PG8H+JSfTevoyIPQdJcVpx2YI5Ed6R1etLEp8QQHJyAFttA8BdEOioMwKLK4Z7e39F66bRtKz1iIQk3Lhcmv/851c+HbsC1951HHmpNZtGP8QHjliGE4t6bRhN7jnCjJ+PM+adlcyZsyvDr7NMmSI0aFDWLRsjtVIZwLx50SQk2HG5NGvWHEQpxebNx+jadQqvv74c37WW8uWL0ahROH5+Fjp1qkK9emUuOlfdumWMwc0xFvF0s7PBKa11M59tYvqjuXtHhmqt12V11kLl6Xro2U06QoDYqeLFxEHyJSgQbqgLO3bDgYNicK1WCSV4FuMcDnn9sgitAE8uv9xL4GubAxdWYkpVZEvUMFp4OudumwdnRPiOhhlN+/Dir+NwWK0E1O6KdfLd3szfG3rD2q9SF8VcfkVQLgcKGPHrWKLr3EL9Q5tAO6l45hBojdIuymw9CxGfQ+db4ewTUmPC5YAUJ4TVQp+IBq3RLVxQUaNOKzgDf7WsR7Ky4LQFsrZS2jbdFgXrajQjulNT4v3hgaI2bnmnH9ToCMMWiPb517cgvCZENmbFoUr0nXcbDpeV9pVPsKi3LJAlW6rj/+F2SUZwOSm1dCz/CygG1dqy9+0kHpkURLnIEgwZ0oSEBDuvvbKENhEnGFR6B+q0HxadzH31d8tinegwJCTiU5Vu9eoDVN49ni96rMS1BfwsmuKxW5n2Tk0cI+9iwtSKJDr8AI3DoVOlWemJiTnL+PHrU380oqIqERn5Ia++GsWoUR0YMOBHKlQozq231sbhcNGu3TfY7S4WL95LkSL+qem3VquFtWuHcPz4BcqWLZqtdOHM2LfvHCVLBqXGn69vcuTpZn2k7PWOBAqp0X1xOJw6DctWw5jXoHsXqb178pR3THyCKBKK+KxZOJ3i2drcK/QD74aO7WDnbnmt/0CptTt7KpSPTH/W3OU2AvmJJMICiuLqUY1NTKQ+A7Ge3ofHqqrAEBp0foFhLe5moH9pogLKiGeLlkSFrs/Dlp/gn2UAKFxI1QeNn8tB5fmvQvRSAEomxmLVGrvVyuYSdSCsl2Sz3TYWtv8MSbFy3BO7saBwVmiO5ZeDqLhjqXN+aM13zKvXmbjAEN5a8JF4xineGrGVzx5CA8HJCdQ68a+8uHethBLWfS3PT/6DjmjArHLtsdv8sCfB8cC6ULkV+AWT0Ocb5j18E7dV3YlVaYl5L3obmm2hyu3tWHC79zMc8VRjRpzoLj8Y0X7gHwgpDlwtBvHhx/soXmQyg+7aiSX4rjQx9ooVi/PIDX9gtYhGzu6Uz6zMmSDuIYgNLWoTNP8oKS4rTz/Vku7dM46jlioVhL+/LAQWLerP4sV7SUiw8+STC0lJeTmNLMzhSNt8MibmbJpjWSyKcuWurJD4q68uY8yY3wkMtPH33w9lmiBx3eCyQuKVF2fPQe9IGV9YJGOXYut2GPqkxHxPnoYk6bSC1QoTPoRhT4PTJaqEt16GRUthwWIJN1gtUn3s4CEJSzz2IIwdk8sTPL5LPL2KzSHqcbSCgzg5zGdsZRwADRlKy4QH4et+Ih0bMFXCESBJGUe2iZFd9RnU7AgPzpHV/OkDYfdSKFMd54E/sbgc2P2C8PdkjwFby9ZkaY0bea37E7Q6uJUFGxaK1tVqg/VT4L+Pye19Zlj8QDvlNt0vEKpHwe4lqccHK+Bke9kabIqoS+/tiwlJjoeoJ8XgJp9PPdSWYfNY/df3bByXwJKk2sy9eQcN6pWCDk/Ce83Q7mMq33MPngmhFSG8tszj23skPp4YK56+xSb/Ou1Ex5enwbcSFx03rgdDhjQRlcmJ3dBqMASHcmbiEIrv+gECQvjv0bb846jNo+NepGTJIDZvPsbTT/9KVFQlXn21Q5Zf67//nmHFiv20bBlJmzZf43C43AVuHr5o7KxZ2xk27BfKlSvK4sX3ERaWuxWwqlUbR0zMWYKD/fj0054FumpYrkjGmjTTrMimzSmW+fmUUsOQ5rtuOQ4TtNYzMj3v9WJ0PbhcUtTm/U9g7Xpo2RRW/wY/zoNBj0BEOVkwmz4zbXqwzQYB/nLXPu5deGBALk/s7Qbyn94/GIb8KAZi2Vg2drBRZe4SLE7YM+R+moVlkHyRHA+j60LSeckIe+aPtOqIPSvhi97gSHRfTBC0fgDWfJEqD9OAU1lYKDhezgAAGn5JREFUW7kJNU/uI/zCKWh6L3QbAXOegx0LwGJDu8MTFxFUEhLPeJ/7LLwBUKI8nPNtNa5g4A/QsA/MfBTWfimzuNGFo2l1rDP+RZ2w4EJh8SymWQPAmZz2GAFFZcHS5ZDFuDpNoUM1EV/vdceGmt8HNTvA9MEAxCb7U+qL4dj8rIx6rh7PuR6D+FNimKu1FY2v1hITLxom34kPFSp8xKFDcQQF2Vi//kFuqFMSVn0qcfeOT180HqQtz88/R3P8eDz9+tUjJOTq395//vmfPPbYAsLDi/LXX0MJD8+85m5+J1eMbqNmmqXZtDmlrvx8HgpleCErLBaRfN37oIQTNm2TUo59e8tWvg5Mm3GxouvZJ6DdjeBngy4d82BiNndlMq3FeEy8HRzJNIyxYHW6QEPjRXEiTknPuYOQcE5kZIe3wG/vQPRi6PGKeJyOJPH+PDiSRMJmj5eU5L9moFwObNpFu70+f4Qbp8PWn7yG2eXgZJFQysSfvdjwtnkQVnwC9gSv15tmjofdFc88wXUN394FrR6A/3tbvN3KDmjtxOa/G/qAnuifKpkD0hlcILKBXN+KT+R4Lgc0WgVn1krL9b3uWOvOBRyw1aaC+1AW5aRPjwqEljnFY7c8C8tOQLxF9r/gjkEpJWnUHg5sEM+50W04nWkX3Vj1GfzyiuSUXzghNZHT8dRTC/nyS5F1tW5dIU2nhuwQHX2aIkX8riiL7OGHmzNwYGP8/a0XqS2uWxyXHpLbXHdG10O1KvBPjNyiRvok8HgWzvxsYvusVqhdA0a/mv1jvzQKPp4AvXvC9C8zluRexJD/ifEoGgYL30xdvba5rKLrRWGt1O6i3fbgYGqZsjxS7ybCty+ERnfAknfF+H3dH0Yfg1pdoemd8Oc0uf0Pry0ecX8p78iND8HcEaKKiF4qhgMADSkX5MfAGoB2pRAWfxYXCqfVhq3zc2KkanaEKfeK0bL6y/l2/Jxuplq896JhEH/aG4rY+B3U6wH3TIYdo8G2S8Yl+eiAIxvB4U3yOLAEdHseAkKgST84fxw2zYLzJ+T837nzlQN8FreSYqmw5kVAvotkpz+zfmwBZ1sAidAPGBskGYL3fnvxd3N8F4zvIo/XTWbhwlm8//4aunSpKoqBRQnuBnVOSEnI8OtdsGAPCQmScbZ+/eEcGd3PPlvP8OGLAPjttwG0bZt177OsuFQxnesKTf43ukopGxDj3gAe11pvzWTs60BPYL3W+pIdza42y+bDvIUSSvBdFHvxGXjG3TR+0D3QrRNUrwpTf4A+N0NIurj7yt/lvXv7Q1Rbkau9/aH8H/xxviRe1KyejQmFVoQ+78F7zdFHtpDoCGTB4VupdO+TNGuMGJRqXqM7mXh+JpnlpHDG4uK9gR+xg+lUPrUfNs+SW+Ui7j5ZSXGQdAHK1YPa3aHLs958ZqcdSlXyKi3O7JckhcRYCSlopyzKdXwKlnyAw5nCieLhxL4STR1P4s3xnd7YrTMFyjcSTxslhuyIlJTEniibskFIWenoq11QPBLqNYKm/SF5Pix9CFaflH38guC+KTCmiZwjKVY83Jqd5f3AYvCaW82xagL87yk5bzJgDQRnEjhSUn/4NODXvSQkuRfuUBBQBoYvFp0wSGnHPyZLPLv5AIg9Ij88KfFwdh8NGoQzZcqt3u8u6kkx+skXoPfbuFyaBQv+oWTJoNTW7G++2YnBg+dQpUqJVC1wdpk9exeJiQ4sFsWyZXuvyOgafNDA5aqTroCc/uw1AL7XWo/IapBSqinQFmgBvKKU6qK1XnyZc8wTQkPhvrsufj3RHfZMsUuSxUvDpZiOwyGLbKf3elOAL1yAm/qKxnfaTDixB4oWFSna3n2SUhyZeRp8xhQNw6H90UD0uWocWBpHs77d0wzZjp1HiCWRtH0hEtCSXjxoBhzaBM3dsYjlH8P2eZL1VbYuzB8JayaJx3s8Wg7ScpAU6zm5R26jUxJEMbD3dzE4rYdiCS6FJe4YEa0HE+Gb6RhSLu1Mts6B1/aJUV8wymt0Pfj5S7LHmklyO1EsErbOFaNWszO02wLbbgIOQt+xEFZLWtlfOCHn+Lw33PEJtB6c9rj7fRonhtUWg79NEoO0e7PfX4TiEfsgcSIEPwskQ+ADYKvh3fe30bDsQ/eHelaMavN7RRkS9Tgc2OhdwAQp6tP3w9SnI19cwrhxf6A1zJhxO7161aRfv3r065e2jkN2eeGFtqxde5DixQPS1FwwXCEuIPHqnzanRrcV0Esp1RHYCjyktc7IQY8CZmuttVLqV6Tq9EVGVyk1FBgKULFi/vj1rlPLW61sw98wf6G3rGNiImzfCc3c3dW19lls095CMOsWS0uhRvVzWBQHYOB09n8/mX8XLuGJep8SGPAZbJ0M9W9JHRIUd5yHN01hVeUmHAuvQfvERNqWqEJd/CREMfd5CA6FFu7VvmJlQbtdvYN/wcl/5PHxXalzZ8N06PYCTOrjLXZz2n1D43LAhO5w9qB4ninxELMaerwG9XrCwQ0SAnG4JSHhdbxe9ppJF19j+yfEqC8cJYqIuc+TarSDS8Ir/0hBIF+sPkZeO0Q7bE8U7z+ygXijGz01cN3H2rlQPH6tUVXboIb8SEBiL7B7ZHWtIeCmi+d3/pg7jq0kfGGxSNnK3Yvhq9vl9Z6vQoenMvwKN248Qny8HT8/C1u3HqdXr5oZjssuXbpUJT7+xSvS5xoyID+GF5RSXwC+90LLgC5a66NKqSlI+CCjHOMigFuIyRkgw1QZd1bHRBD1Qs6mnjec9yllqjU89YIYUq2hbDjU80nSCgmB+TPhm+mi6S3mXuMIDoaO7S9zAkElqD74KarEL8QSk4hSAXLL70PV8Tfx3tkDOAGrzR+rPVl6qHV7QVbRXQ5RNOxeDC3ug7hjchuvXZJmGxQqBtKR7M3EanQHbPw+TWYW/kW8z4/vRmK88XIOkDjumDNQsZkYy7gjojA4sBE+jhKNb0QDMcq+7FsH1dvJIp7305Z/kuLg90lye188Qm75u70ADXrLYps9SQz/0W1S9EdZ4eVd7gUwj7etZWHRmSJKgp6j4Le34cOWMGw6BH8P1jrgn/YOIpUer8GFk2KwO/tkE8as9X5muxdnanTffbcr+/fPonTpYJGj5QLG4OYB+TG8oLVO05NBKRWgtfYsIW8Aaly8FwAXILX1QVEKULpxv1vh66miaGjTClatFYNbqwZsWyfSMV86d5Att7H2+wi+HypeastBad+MO4rVkYzV6g8OuxiX9VPEOLUcJE0xbQFQo4PEJ/cs95FvKajbA1oPgfGdvMcsXVVuq5FOFjS7VwrmRC+CCs1gy/9g8XtuD9BtIItLxwKS46UuRNwRURiciZHto7YSmsACuGQvmx8pN7QjoFo72T/2cNprczlgnrvW7Yld8O8KiDsKVdtAmZrQ9iFRPDxbTK7bL1Biw+VuEK97zwoxlNXaSRilWlvRLieclnjwxkXQ5RIi65AwGPzfi19veZ9408nnJc07Exo2LMuuXY9lfQ7DtSc/eroZMFUp9RawDeiDCIIzYiOyJvwD0BDYd7kTvNr4+8PS+fI4Nha694WYvTD2nYsNbp4SXgeeWpXxe/dNg19eg6pt5TY7wQFRT8h7XUdAy/tFnhV7CF4uL0YioBgEFhVj2nWEeIi+7FyQ2ueMsNrwf2/J45YD5d+IG2RR6f2W4u3W6wl3jIcN38MPQ70hiTToNK9ri4XNUYFsiJrCbadbUjLhjIQN/IPl3BklX7ic4v3OGSHe+ez/QMvBkhiy6G1oeKt8Vks/lGQMpx0WviGLco8vkduURWMkrIKGyi0z/8xdLlFdBJcUI58ei00WO2t0EH3wpUhJlAam4bWlkLwh/1EAjO4o4DvkPm6u1nqxO+f4Xa31EJ9xq4G3lVIfI2XOMgic5X+KF4d1S678OKfPwOdfQ52aogW+Yur2kA3gljFirAJ8gsfFysq/W+ZAcpwYrnJ14ckVaY9T5Ua5RQc4usP7ujOTe65SVeD1feJZxh4Rg/nX95kYXETeleDtKOsIUCQWcVHkTApnL6ymJEr2TbS7e8YdJO3/AiWx4d7vwPst3HNLhvXfQqtBkljhYdMsb0xZO+GvGXDzm1KEvctz0kEjuASUyezmDPh5JKyeIB7QfVOk1ZGH+DPwbmO5cyhdFZ69hKjeniTj445JkfcnlmdTO2i4ajiBuKt/2hzd9mutt2mtG2it62utX3K/diadwUVr7QK6AKuAHlrrvbk24wLI7QPg9XdgwFBYtjKXD261pTW4vtTuKmEGW4BkZYHcfi8fKzHLuyZJ3NY/WGKsVn9AiTY3I6/T6RB1w3dD4LPuMLoetBjo1hGno+0wGJBW82qzW2i+IJ7b3j9BubKDoP1j7splWsIMzfp7B1tsok547i8oW0eSIDzMfBR+T1fkqcsIScpQVon5lqggJTJBjF2l5lkbXPCqNpx2OJaucti5Q+BIYcPBEL5cZCP23CWWvc/ulwLw9kSJYWf2w2S4djiB2GxuuUie3TBrrROBWXl1/ILE2XPuspF+F1c7y1MiG8KrMWJISkTC0e0w8RbxfDf8AMPXwYvbJaOtQjN4q7Ys2p3cA1vnQePbRXv68yviPR78W+RfnjAESjzJd07DG7XEcCorDHVnsS3/WORgcYdB2bA4nVg0UmgkJRh6vSEGceUnEjhvNVhkXyf/ldvxdo/KD8HhLZLMsXsxnq4a/LsK2gz1XmuDW2DMOfGEj2yRBbyc3tL3fgemDBDvulW6OHq5G9gVdiftPyoDFhsTu01jyZL7Mk/nLV1d4sm7F8t1ZfTDZLi2XCNP16SnXAW++wqGj4T6dSUF+aoSHCobiHcL4nVdcHejLV5ONhBDdeGkrM57uvoufEPSXH3TcS3uP5tKzaFCUzFuwSXE6Nr8wZ4iKb4e705ZJeusehT8/oXUfQgJk/c6Pwc1OkHxcInNPrIQ/vhWjh1YDN6s5a6t4JTj2NyGNCTMp1kbMPlu2Dwb6nSX7DZrBn/aK8dLbLhcPenGHFBUrlW5b/gi6sPzmzL+HC0WDjV6DkvAD8TH2/nzzyOEhb3P/Pl30blz1QzGW6Uovcspjw35j4IQXjBcHnVrwy+zYMyobLT5yUsiG3k9rqrtYVQNeC5U9KwgC3T9v4DHl0lWGUjs1mNwPYtv1aPgvTgpDHM6RoxZ7zFuKVqyO5vLV1frlDTeqMfhxW1SFAZg4wwYWRYm9/ceu3ikHD+wGEwf5L7dT3GnDbsF1PZEkY/tWe49zubZ8njXIhhZHl6KEI/dl99Gizri5B7ZN/ZOOGmD2H5pqxtlQqdOVRgwoAGhodL9w5GSzNwpS7Le1xjc/IvH6GZny0WMp3s9EbPau0i2bY7EaF12KSlZ5yaRXzXpl3afHq+K5Epr8VYHzvD+ciSdh4/aiGzNL0B0t9ol2W9P/y4JFxumy7jm9188n5XjZT7J8SJzqx4l4Y2Vn3iP5dEJ2wJlrs4UMdBag79bQbDjF+8xtQZcEpeeMgCe8TaEpFY3yZaz2CCiAiTPBjQk/wj6BKisOy9YLIoJE3px5503cGuvyfxx+ySqhZ6HyYslC9BQsDDhBUOeU6m5GFaXQ2ow7PpVbsN9V+nTU6Y6vBwtHm2llmld9eQLYhydKXIbHV4LTkZD7W6SMFHuBvh7Fvg5YNUnYkzr3Qx3fyXHaTlQPGClRGmxda7ItVISvF19AUpVhTP75LnFD9oMEeWFPVHkZO0flXq4aKjewVts59zBtNdyz9cS7w2tIOGQM7XBGQPWyqBKZ/tjjIqqzMGNPQn+cizKbpe5+4Y6DAUDO3DokqNyHWN0rydCwuHlfyS1tVQVicEmxkqMMyt8474edi6U5I0S5cEvGDo9LS3mzx+HYu6x8aeluLrvyv2WH6HzcDnnjQ9A/V6w8lOpdeB0ioF12kXVcO6QeLdxR6HTM7D6c2h8B/T5AN5tJOUig0PhpR3w9kkxevZE+LSbpDjf8q6c05EMR7ZK3QlP2ASg5AZw7ARbnYt1y5egSNWG7mI+26DZXcbgFkSMp2u4KgQUgQD3wk+J8rJdDj8OFwPrFyxJEp7iOp4sNRDFRNuHJcSARcpN2gLSnjMkXAzqyT1S2+HgBvFoe4+BtZNEzdD1BfFmzx0SA3wqWhQO2ikGddlYURuEuAuOP+3TCtrlksy4U3vkXM9vkcU+kIaDfo3EW7Yp7+vZwRYA/1kniSdBxS/vMzRcWzySsVxCKRUOzNJaX1yD1QdjdA2XR+VWssimXd6SiBnR5z3Z9qyCL2+VBbbzx9IaqqDiMPA7ybI74K4UtmEaPLHMO2bxu7BptoRG/AKlCPuaL8UT/m00/DlVFunSk3JB6jRol3jGcUelbnDyBfGID2+W0EBgMYn/lqqS/c/AYjEGtyCTi56uUioU+BapO5MlRr1guDzu/EIWj4b/IVW+LsWq8eIVnj8uxjIjGt0mMi6rP7R7JO17IWGyAGb1l/DFrR9Ihp3VXd3sXCbBucBiUo9CWSWeHOquZhe9REIQLod4zPZEr4rDcH2Qu+oFJ9A/O6ONp2vInAMbYf6LUKkV9HwtbdzSYpWMt+xSuzvs/FUe18ik31FEfXjziCzKxawW77Z4JMx5VrLJbn1f4sOt3HV0IxtKVtuOn6UyWGb0/0w2XyIbyWKdp7WQzR9qdYHZT4mWuG4PGDzrGmv8DHlKzjzd0kop39zvie4qiQBoreMge9XgjNE1ZM63d4mEa/+fUL091Op86X3OnxBjWbKyxGE9f4StB0OlFmLcwrKoL2sLkALsX/eTBTVlEUObkiiysdYPeMcqJVltvd7I+bWVrAQvbZfrC60k7eYtVqm9AFI859SerOdqKNjoZEjOdoWCU6YxpSHvKVIazrnjtsEls7fPdw9InzWrvxTeaXy7972IG7J3jMSzYmxdDlExWP0k7hrZMOfXkBUh4bJ50FrSoY/vgCKlpH6DofCinBBwNntjMyhFcrkYo2vInAd/kpTc8g2hQuPs7eNbb9d1mXXzqneQFjn71kLP10X1EFpRWhHlJUrJ4t2RrVKO0T/o0vsYCi4WJ/hn0+jmIsboGjInJEyaWOaEe76WvmilqkDjfpcenxHK3Q7narN3rSz21epqdLfXA8oBAedy9ZBa6w6XGmOMriF3KR4Bd35+7c6vtbQdOndYukwEFsveflvmwLSBUim60zNZdoYwFBJyEl7IRYzRNRQutvwk9XZdDji0EQb+kPb9f5aLNrf5vRK39XB4i5SFdDlFtWEo/FiTIeTql/o2RtdQuEg8h7QJskN8Oi/m8Bbpduxywt//TZu51uZB2LVQstNuvgw1hKHgYTxdgyEXaHaPLISdPSCZcL5cOCGxWmeKtNHxpVhZqYxmuH6wOHM9ppsdjNE1FB6O7YRv+ovMbMjstHUgQIqlt3kI9q6DW965NnM05B+Uw3i6BsMVseA1OLFbUn5XfQa93kz7vsUiLXkMBnB7uvnc6CqlhiH5xQAlgD+01g9lMM4GxLg3gMe11luvZKIGwyWp0BR2/SYy4chGlxxuuM5RDvDP5+EFrfUEYAKAUuoTpKpORjQAvtdaj7iy6RkMOaDzs1ChiZSbrHpjzvd32mHWk1II57ax2SvkYyi4WFOgWAFRLyilIoFwrfWGTIa0AnoppToCW4GHtNaXmZ5kMGQTpaRozeWyabZofO0J8P0QGL4+9+ZmyH+4LJCc3azDlEsPySZZGl2l1BdALZ+XlmqtRwGP4vZ4M+FPoIvW+qhSagrQE5ibwfGHAkMBKlasmMOpGwy5jKc7hi1QqpsZCjfaAknB2Ryce9XOszS6mcRrLUBH4KUsdt2itfaUiNgA1Mjk+BOBiQDNmjW7dDtWgyEvqR4Fg36AU/9C8wHXejaGvMalcuDp5h6XE15ohyygZWUkpyql3gK2AX2A0ZczOYPhqlOn+7WegeFqoXMSXsg9LsfodgdWep4opeoCd2utfZPVRwHfIZnsc7XWi69olgaDwZDbuHISXsg9cmx0tdYvpnu+AxiZ7rVtiILBYDAY8idOG8SVuvS4XMYkRxgMhusTbYGkghFeMBgMhoJPjiRjuYcxugaD4fpEWyC5AMR0DQaDoVCQi+oFpdRXQF3gZ631m1mNNUbXYDBcnzitEHvlC2lKqb6AVWvdWin1tVKqhtb6n0zHZy23vXoopU4C+6/1PPKI0sCpaz2JPMRcX8GnoF1jJa11mSs5gFJqIXLd2SEQSPJ5PtGd3IVSahywUGv9i1LqTiBIa/1NZgfKN57ulX6A+Rml1AatdbNrPY+8wlxfwed6uMb0aK1vyqVDFQEOux+fAZpkNdiSSyc1GAyG65ULgCc4XJRL2FVjdA0Gg+HK2Ai0dT9uCOzLanC+CS8UciZe6wnkMeb6Cj7XwzXmFT8Bq5RSEUAPpLRtpuSbhTSDwWAoqCilQoGuwEqt9bEsxxqjazAYDFcPE9M1GAyGq4gxunmMUuorpdRapdTIS48uWCilbEqpA0qp5e6t/rWeU26hlApXSq1yP/ZTSs1TSv2ulBp8reeWG6S7vkil1CGf77HQyjfzA8bo5iG+mSpAVaVUhh00CjCeBqQd3Fuh6Pjsjs99i+gvAR4HNmqt2wC3K6VCrtnkcoEMrq8l8JbP93jy2s2u8GOMbt7SAZjpfvwbXllJYcHTgHS926MvLGoYJ9AfiHM/74D3e1wJFPQkgvTX1woYopT6SyllurzkMcbo5i3pM1XCr+Fc8gJPA9IWgB/SgLTAo7WO01r7diIsVN9jBte3APlhaQ60VkqZBgR5iDG6eUuOMlUKIFu01kfdjzNtQFoIKOzf4xqt9XmttRP4m8L7PeYLCtsfT34jR5kqBZCpSqmGSikr0oB087WeUB5R2L/HX5VS5ZRSwUA3pKGsIY8oLDG4/EqOMlUKINdLA9JvgV+UUu2Qmql/XOP55DavA8uAFOBzrfXuazyfQo1JjshjcpKpYsi/uH842wK/pouHGgw5whhdg8FguIqYmK7BYDBcRYzRNRgMhquIMboGg8FwFTFG12AwGK4ixugaDAbDVeT/AVA0R6vMfFvXAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import helper as hlp\n",
    "\n",
    "data = np.genfromtxt(\"zip.train\")\n",
    "X = data[:, 1:]\n",
    "y = data[:, 0]\n",
    "#PCA分解with centering\n",
    "pca = hlp.PCA_(n_components=2)\n",
    "X_pca = pca.fit_transform(X)\n",
    "\n",
    "plt.scatter(X_pca[:, 0], X_pca[:, 1], s=5, c=y, cmap='gist_ncar')\n",
    "plt.colorbar()\n",
    "plt.title(\"digits data with 2 components PCA with centering\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#PCA分解without centering\n",
    "pca = hlp.PCA_(n_components=2)\n",
    "X_pca = pca.fit_transform(X, flag=2)\n",
    "plt.scatter(X_pca[:, 0], X_pca[:, 1], s=5, c=y, cmap='gist_ncar')\n",
    "plt.colorbar()\n",
    "plt.title(\"digits data with 2 components PCA without centering\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problem 9.8 (Page 39)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import helper as hlp\n",
    "\n",
    "data = np.genfromtxt(\"zip.train\")\n",
    "X = data[:, 1:]\n",
    "#中心化\n",
    "X -= np.mean(X, axis=0)\n",
    "y = data[:, 0]\n",
    "#选择的标签\n",
    "l = 1\n",
    "#划分数据\n",
    "Xpos = X[y == l]\n",
    "Xneg = X[y != l]\n",
    "#对每一类分别使用PCA，flag=2表示pca中不使用中心化\n",
    "pca = hlp.PCA_(n_components=1)\n",
    "pca.fit(Xpos, flag=2)\n",
    "z1 = pca.transform(X)\n",
    "\n",
    "pca = hlp.PCA_(n_components=1)\n",
    "pca.fit(Xneg, flag=2)\n",
    "z2 = pca.transform(X)\n",
    "\n",
    "#作图\n",
    "plt.scatter(z1[y == l], z2[y == l], s=5)\n",
    "plt.scatter(z1[y != l], z2[y != l], s=5)\n",
    "plt.title(\"+1 digits VS -1 digits with 2 components PCA\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problem 9.10 (Page 40)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "E1 = 2.9848477689390487\n",
      "E2 = 3.3734459718878087\n",
      "E_out = 0.2671906269590378\n"
     ]
    },
    {
     "data": {
      "image/png": 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XzTdLmyJPNkSwS5ImtxHm2CVJr4DBLkmNMdglqTEGuyQ1xmCXpMb8Hxb2wKXUuoUxAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "E1_mean = 1.865415167353018\n",
      "E2_mean = 2.3127315449440284\n",
      "E_out_mean = 0.2877558958424026\n"
     ]
    }
   ],
   "source": [
    "#### (b)\n",
    "import numpy as np\n",
    "from numpy.linalg import inv\n",
    "import matplotlib.pyplot as plt\n",
    "import helper as hlp\n",
    "\n",
    "#### (i)\n",
    "N = 40\n",
    "d = 5\n",
    "k = 3\n",
    "\n",
    "def data(N, d):\n",
    "    \"\"\"\n",
    "    生成数据集\n",
    "    \"\"\"\n",
    "    X = np.random.randn(N, d)\n",
    "    w = np.random.randn(d)\n",
    "    epsilon = np.random.randn(N) * 0.5\n",
    "    y = X.dot(w) + epsilon\n",
    "    return w, X, y\n",
    "\n",
    "#### (ii)\n",
    "#Algorithm 1\n",
    "def Algorithm_1(X, y, k):\n",
    "    pca = hlp.PCA_(n_components=k)\n",
    "    pca.fit(X)\n",
    "    Z = pca.fit_transform(X)\n",
    "    e1 = []\n",
    "    N, d = X.shape\n",
    "    for i in range(N):\n",
    "        #每轮选择的数据下标\n",
    "        index = np.array([True] * N)\n",
    "        index[i] = False\n",
    "        #划分数据\n",
    "        Z0 = Z[i]\n",
    "        y0 = y[i]\n",
    "        Z1 = Z[index]\n",
    "        y1 = y[index]\n",
    "        w = inv(Z1.T.dot(Z1)).dot(Z1.T).dot(y1)\n",
    "        e1.append((Z0.dot(w) - y0) ** 2)\n",
    "    return np.mean(e1)\n",
    "\n",
    "#Algorithm 2\n",
    "def Algorithm_2(X, y, k):  \n",
    "    e2 = []\n",
    "    \n",
    "    N, d = X.shape\n",
    "    for i in range(N):\n",
    "         #每轮选择的数据下标\n",
    "        index = np.array([True] * N)\n",
    "        index[i] = False\n",
    "        #划分数据\n",
    "        X0 = X[i].reshape(1, -1)\n",
    "        y0 = y[i]\n",
    "        X1 = X[index]\n",
    "        y1 = y[index]\n",
    "        #训练\n",
    "        pca = hlp.PCA_(n_components=k)\n",
    "        pca.fit(X1)\n",
    "        Z1 = pca.transform(X1)\n",
    "        w = inv(Z1.T.dot(Z1)).dot(Z1.T).dot(y1)\n",
    "        \n",
    "        Z0 = pca.transform(X0)\n",
    "    \n",
    "        e2.append((Z0.dot(w) - y0) ** 2)\n",
    "    return np.mean(e2)\n",
    "\n",
    "#### (iii)\n",
    "def E_out(X, y, w):\n",
    "    #计算结果\n",
    "    w0 = inv(X.T.dot(X)).dot(X.T).dot(y)\n",
    "    #生成新的数据来模拟Eout\n",
    "    d = X.shape[1]\n",
    "    N = 10000\n",
    "    X1 = np.random.randn(N, d)\n",
    "    epsilon = np.random.randn(N) * 0.5\n",
    "    y1 = X1.dot(w) + epsilon\n",
    "    y0 = X1.dot(w0)\n",
    "    return np.mean((y1 - y0) ** 2)\n",
    "\n",
    "#### (iv)\n",
    "w, X, y = data(N, d)\n",
    "print(\"E1 =\", Algorithm_1(X, y, k))\n",
    "print(\"E2 =\", Algorithm_2(X, y, k))\n",
    "print(\"E_out =\", E_out(X, y, w))\n",
    "\n",
    "\n",
    "#### (v)\n",
    "M = 1000\n",
    "E1 = []\n",
    "E2 = []\n",
    "Eout = []\n",
    "for i in range(M):\n",
    "    w, X, y = data(N, d)\n",
    "    E1.append(Algorithm_1(X, y, k))\n",
    "    E2.append(Algorithm_2(X, y, k))\n",
    "    Eout.append(E_out(X, y, w))\n",
    "    \n",
    "plt.hist(E1)\n",
    "plt.title(\"E1\")\n",
    "plt.show()\n",
    "plt.hist(E2)\n",
    "plt.title(\"E2\")\n",
    "plt.show()\n",
    "plt.hist(Eout)\n",
    "plt.title(\"Eout\")\n",
    "plt.show()\n",
    "print(\"E1_mean =\", np.mean(E1))\n",
    "print(\"E2_mean =\", np.mean(E2))\n",
    "print(\"E_out_mean =\", np.mean(Eout))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problem 9.14 (Page 42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "#(a)\n",
    "def f(N):\n",
    "    #生成数据\n",
    "#    N = 40\n",
    "    X = np.random.randn(N)\n",
    "    r = np.sign(np.random.rand(N) - 0.5)\n",
    "    \n",
    "    #寻找阈值\n",
    "    X1 = np.sort(X)\n",
    "    X2 = (X1[1:] + X1[:-1]) / 2\n",
    "    X2 = np.append(X1[0] - 1, X2)\n",
    "    X2 = np.append(X2, X1[-1] + 1)\n",
    "    \n",
    "    #计算结果，向量化计算\n",
    "    temp = np.sign(X1.reshape(-1, 1) - X2)\n",
    "    result = np.mean(temp != r.reshape(-1, 1), axis=0)\n",
    "    error = np.min(result)\n",
    "    \n",
    "    return 1 / 2 - error\n",
    "\n",
    "N = np.arange(1, 101)\n",
    "Error = []\n",
    "for n in N:\n",
    "    Error.append(f(n))\n",
    "plt.plot(N, Error)\n",
    "plt.title(\"penalty VS N\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#(b)\n",
    "m = 100\n",
    "Error = []\n",
    "for n in N:\n",
    "    error = []\n",
    "    for _ in range(m):\n",
    "        error.append(f(n))\n",
    "    Error.append(np.mean(error))\n",
    "plt.plot(N, Error)\n",
    "plt.title(\"mean penalty VS N\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#(c)\n",
    "N1 = 1 / np.sqrt(N)\n",
    "N2 = np.sqrt(8 * np.log((4 * ((2 * N) ** 2 + 1))) / N)\n",
    "plt.plot(N, Error, label=\"Rademacher optimism penalty\")\n",
    "plt.plot(N, N1, label=\"$1/\\sqrt{N}$\")\n",
    "plt.plot(N, N2, label=\"VC penality\")\n",
    "plt.title(\"mean penalty VS N\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problem 9.22 (Page 47)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from numpy.linalg import inv\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "X = np.array([[1, 0.51291],\n",
    "     [1, 0.46048],\n",
    "     [1, 0.3504],\n",
    "     [1, 0.095046],\n",
    "     [1, 0.43367],\n",
    "     [1, 0.70924],\n",
    "     [1, 0.11597]])\n",
    "y = np.array([0.36542, 0.22156,\n",
    "     0.15263, 0.10355,\n",
    "     0.10015, 0.26713,\n",
    "     2.3095])\n",
    "\n",
    "def l(X, y, Lambda):\n",
    "    N, d = X.shape\n",
    "    #计算\n",
    "    w = inv(X.T.dot(X) + Lambda * np.eye(d)).dot(X.T).dot(y)\n",
    "    H = X.dot(inv(X.T.dot(X) + Lambda * np.eye(d))).dot(X.T)\n",
    "    y_hat = X.dot(w)\n",
    "    \n",
    "    N = X.shape[0]\n",
    "    H1 = np.diag(H)\n",
    "    Ecv = np.mean(((y - y_hat) / (1 - H1)) ** 2)\n",
    "    \n",
    "    #最后一个点\n",
    "    m = N - 1\n",
    "    #分子\n",
    "    e1 = y_hat - y + (y_hat[m] - y[m]) / (1 - H[m][m]) * H[m, :]\n",
    "    #分母\n",
    "    e2 = 1 - H1 - H[m, :] ** 2 / (1 - H[m][m])\n",
    "    Ecv_m = 1 / (N - 1) * np.sum((e1 / e2) ** 2) - \\\n",
    "            1 / (N - 1) * ((y_hat[m] - y[m]) / (1 - 2 * H[m][m])) ** 2\n",
    "    return Ecv - Ecv_m\n",
    "\n",
    "Lambda = np.linspace(0, 10, num=300)\n",
    "leverage = []\n",
    "for i in Lambda:\n",
    "    leverage.append(l(X, y, i))\n",
    "\n",
    "plt.scatter(X[:, 1], y)\n",
    "plt.show()\n",
    "\n",
    "plt.plot(Lambda, leverage)\n",
    "plt.xlabel(\"$\\lambda$\")\n",
    "plt.ylabel(\"leverage\")\n",
    "plt.title(\"$\\lambda$ VS leverage\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Problem 9.23 (Page 48)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
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     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from numpy.linalg import inv\n",
    "\n",
    "data = np.genfromtxt(\"features.train\")\n",
    "#预处理数据\n",
    "N = 500\n",
    "X = data[:, 1:][:N]\n",
    "y = data[:, 0][:N]\n",
    "y = (y == 1).astype(\"double\")\n",
    "\n",
    "def l(X, y, Lambda):\n",
    "    N, d = X.shape\n",
    "    #计算\n",
    "    w = inv(X.T.dot(X) + Lambda * np.eye(d)).dot(X.T).dot(y)\n",
    "    H = X.dot(inv(X.T.dot(X) + Lambda * np.eye(d))).dot(X.T)\n",
    "    y_hat = X.dot(w)\n",
    "    \n",
    "    N = X.shape[0]\n",
    "    H1 = np.diag(H)\n",
    "    Ecv = np.mean(((y - y_hat) / (1 - H1)) ** 2)\n",
    "    Ecvm = np.array([])\n",
    "    \n",
    "    for m in range(N):\n",
    "        #分子\n",
    "        e1 = y_hat - y + (y_hat[m] - y[m]) / (1 - H[m][m]) * H[m, :]\n",
    "        #分母\n",
    "        e2 = 1 - H1 - H[m, :] ** 2 / (1 - H[m][m])\n",
    "        Ecv_m = 1 / (N - 1) * np.sum((e1 / e2) ** 2) - \\\n",
    "                1 / (N - 1) * ((y_hat[m] - y[m]) / (1 - 2 * H[m][m])) ** 2\n",
    "        Ecvm = np.append(Ecvm, Ecv_m)\n",
    "    return Ecv - Ecvm\n",
    "\n",
    "Lambda = 0\n",
    "#计算影响\n",
    "leverage = l(X, y, Lambda)\n",
    "#找到影响最大的10个点\n",
    "label = leverage.argsort() > N - 9\n",
    "#作图\n",
    "plt.scatter(X[y==1][:, 0], X[y==1][:, 1], s=1, c=\"r\", label=\"one\")\n",
    "plt.scatter(X[y!=1][:, 0], X[y!=1][:, 1], s=1, c=\"b\", label=\"not one\")\n",
    "plt.scatter(X[:, 0][label], X[:, 1][label], color='', marker='o', edgecolors='g', s=50)\n",
    "plt.title(\"leverage with $\\lambda={}$\".format(Lambda))\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  }
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